Find the Degree f(x)=(x+2)^4(x-1)^3(x-3)

$f (x) = {(x + 2)}^{4} {(x - 1)}^{3} (x - 3)$

Simplify and reorder the polynomial.

Use the Binomial Theorem.

$(x^{4} + 4 x^{3} \cdot 2 + 6 x^{2} \cdot 2^{2} + 4 x \cdot 2^{3} + 2^{4}) {(x - 1)}^{3} (x - 3)$

Simplify each term.

Multiply $2$ by $4$ .

$(x^{4} + 8 x^{3} + 6 x^{2} \cdot 2^{2} + 4 x \cdot 2^{3} + 2^{4}) {(x - 1)}^{3} (x - 3)$

Raise $2$ to the power of $2$ .

$(x^{4} + 8 x^{3} + 6 x^{2} \cdot 4 + 4 x \cdot 2^{3} + 2^{4}) {(x - 1)}^{3} (x - 3)$

Multiply $4$ by $6$ .

$(x^{4} + 8 x^{3} + 24 x^{2} + 4 x \cdot 2^{3} + 2^{4}) {(x - 1)}^{3} (x - 3)$

Raise $2$ to the power of $3$ .

$(x^{4} + 8 x^{3} + 24 x^{2} + 4 x \cdot 8 + 2^{4}) {(x - 1)}^{3} (x - 3)$

Multiply $8$ by $4$ .

$(x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 2^{4}) {(x - 1)}^{3} (x - 3)$

Raise $2$ to the power of $4$ .

$(x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16) {(x - 1)}^{3} (x - 3)$

Use the Binomial Theorem.

$(x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16) (x^{3} + 3 x^{2} \cdot - 1 + 3 x {(- 1)}^{2} + {(- 1)}^{3}) (x - 3)$

Simplify each term.

Multiply $- 1$ by $3$ .

$(x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16) (x^{3} - 3 x^{2} + 3 x {(- 1)}^{2} + {(- 1)}^{3}) (x - 3)$

Raise $- 1$ to the power of $2$ .

$(x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16) (x^{3} - 3 x^{2} + 3 x \cdot 1 + {(- 1)}^{3}) (x - 3)$

Multiply $3$ by $1$ .

$(x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16) (x^{3} - 3 x^{2} + 3 x + {(- 1)}^{3}) (x - 3)$

Raise $- 1$ to the power of $3$ .

$(x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16) (x^{3} - 3 x^{2} + 3 x - 1) (x - 3)$

Expand $(x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16) (x^{3} - 3 x^{2} + 3 x - 1)$ by multiplying each term in the first expression by each term in the second expression.

$(x^{4} x^{3} + x^{4} (- 3 x^{2}) + x^{4} (3 x) + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Simplify terms.

Simplify each term.

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{4 + 3} + x^{4} (- 3 x^{2}) + x^{4} (3 x) + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $4$ and $3$ .

$(x^{7} + x^{4} (- 3 x^{2}) + x^{4} (3 x) + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{7} - 3 x^{4} x^{2} + x^{4} (3 x) + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$(x^{7} - 3 (x^{2} x^{4}) + x^{4} (3 x) + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{7} - 3 x^{2 + 4} + x^{4} (3 x) + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $2$ and $4$ .

$(x^{7} - 3 x^{6} + x^{4} (3 x) + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{7} - 3 x^{6} + 3 x^{4} x + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

$(x^{7} - 3 x^{6} + 3 (x \cdot x^{4}) + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x$ by $x^{4}$ .

Raise $x$ to the power of $1$ .

$(x^{7} - 3 x^{6} + 3 (x^{1} x^{4}) + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{7} - 3 x^{6} + 3 x^{1 + 4} + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $1$ and $4$ .

$(x^{7} - 3 x^{6} + 3 x^{5} + x^{4} \cdot - 1 + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Move $- 1$ to the left of $x^{4}$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - 1 \cdot x^{4} + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Rewrite $- 1 x^{4}$ as $- x^{4}$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{3} x^{3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 (x^{3} x^{3}) + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{3 + 3} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $3$ and $3$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} + 8 x^{3} (- 3 x^{2}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} + 8 \cdot - 3 x^{3} x^{2} + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} + 8 \cdot - 3 (x^{2} x^{3}) + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} + 8 \cdot - 3 x^{2 + 3} + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $2$ and $3$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} + 8 \cdot - 3 x^{5} + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $8$ by $- 3$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 8 x^{3} (3 x) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 8 \cdot 3 x^{3} x + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 8 \cdot 3 (x \cdot x^{3}) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 8 \cdot 3 (x^{1} x^{3}) + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 8 \cdot 3 x^{1 + 3} + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $1$ and $3$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 8 \cdot 3 x^{4} + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $8$ by $3$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} + 8 x^{3} \cdot - 1 + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $- 1$ by $8$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{2} x^{3} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 (x^{3} x^{2}) + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{3 + 2} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $3$ and $2$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} + 24 x^{2} (- 3 x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} + 24 \cdot - 3 x^{2} x^{2} + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} + 24 \cdot - 3 (x^{2} x^{2}) + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} + 24 \cdot - 3 x^{2 + 2} + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $2$ and $2$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} + 24 \cdot - 3 x^{4} + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $24$ by $- 3$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 24 x^{2} (3 x) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 24 \cdot 3 x^{2} x + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 24 \cdot 3 (x \cdot x^{2}) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 24 \cdot 3 (x^{1} x^{2}) + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 24 \cdot 3 x^{1 + 2} + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $1$ and $2$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 24 \cdot 3 x^{3} + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $24$ by $3$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} + 24 x^{2} \cdot - 1 + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $- 1$ by $24$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x \cdot x^{3} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 (x^{3} x) + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 (x^{3} x^{1}) + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{3 + 1} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $3$ and $1$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} + 32 x (- 3 x^{2}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} + 32 \cdot - 3 x \cdot x^{2} + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} + 32 \cdot - 3 (x^{2} x) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} + 32 \cdot - 3 (x^{2} x^{1}) + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} + 32 \cdot - 3 x^{2 + 1} + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Add $2$ and $1$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} + 32 \cdot - 3 x^{3} + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $32$ by $- 3$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 32 x (3 x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 32 \cdot 3 x \cdot x + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 32 \cdot 3 (x \cdot x) + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $x$ by $x$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 32 \cdot 3 x^{2} + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $32$ by $3$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} + 32 x \cdot - 1 + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $- 1$ by $32$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} + 16 (- 3 x^{2}) + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $- 3$ by $16$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 16 (3 x) + 16 \cdot - 1) (x - 3)$

Multiply $3$ by $16$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x + 16 \cdot - 1) (x - 3)$

Multiply $16$ by $- 1$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x - 16) (x - 3)$

Simplify by adding terms.

Combine the opposite terms in $x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} - 24 x^{5} + 24 x^{4} - 8 x^{3} + 24 x^{5} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x - 16$ .

Add $- 24 x^{5}$ and $24 x^{5}$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} + 24 x^{4} - 8 x^{3} + 0 - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x - 16) (x - 3)$

Add $x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} + 24 x^{4} - 8 x^{3}$ and $0$ .

$(x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{6} + 24 x^{4} - 8 x^{3} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x - 16) (x - 3)$

Add $- 3 x^{6}$ and $8 x^{6}$ .

$(x^{7} + 5 x^{6} + 3 x^{5} - x^{4} + 24 x^{4} - 8 x^{3} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x - 16) (x - 3)$

Add $- x^{4}$ and $24 x^{4}$ .

$(x^{7} + 5 x^{6} + 3 x^{5} + 23 x^{4} - 8 x^{3} - 72 x^{4} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x - 16) (x - 3)$

Subtract $72 x^{4}$ from $23 x^{4}$ .

$(x^{7} + 5 x^{6} + 3 x^{5} - 49 x^{4} - 8 x^{3} + 72 x^{3} - 24 x^{2} + 32 x^{4} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x - 16) (x - 3)$

Add $- 49 x^{4}$ and $32 x^{4}$ .

$(x^{7} + 5 x^{6} + 3 x^{5} - 17 x^{4} - 8 x^{3} + 72 x^{3} - 24 x^{2} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x - 16) (x - 3)$

Add $- 8 x^{3}$ and $72 x^{3}$ .

$(x^{7} + 5 x^{6} + 3 x^{5} - 17 x^{4} + 64 x^{3} - 24 x^{2} - 96 x^{3} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x - 16) (x - 3)$

Subtract $96 x^{3}$ from $64 x^{3}$ .

$(x^{7} + 5 x^{6} + 3 x^{5} - 17 x^{4} - 32 x^{3} - 24 x^{2} + 96 x^{2} - 32 x + 16 x^{3} - 48 x^{2} + 48 x - 16) (x - 3)$

Add $- 32 x^{3}$ and $16 x^{3}$ .

$(x^{7} + 5 x^{6} + 3 x^{5} - 17 x^{4} - 16 x^{3} - 24 x^{2} + 96 x^{2} - 32 x - 48 x^{2} + 48 x - 16) (x - 3)$

Add $- 24 x^{2}$ and $96 x^{2}$ .

$(x^{7} + 5 x^{6} + 3 x^{5} - 17 x^{4} - 16 x^{3} + 72 x^{2} - 32 x - 48 x^{2} + 48 x - 16) (x - 3)$

Subtract $48 x^{2}$ from $72 x^{2}$ .

$(x^{7} + 5 x^{6} + 3 x^{5} - 17 x^{4} - 16 x^{3} + 24 x^{2} - 32 x + 48 x - 16) (x - 3)$

Add $- 32 x$ and $48 x$ .

$(x^{7} + 5 x^{6} + 3 x^{5} - 17 x^{4} - 16 x^{3} + 24 x^{2} + 16 x - 16) (x - 3)$

Expand $(x^{7} + 5 x^{6} + 3 x^{5} - 17 x^{4} - 16 x^{3} + 24 x^{2} + 16 x - 16) (x - 3)$ by multiplying each term in the first expression by each term in the second expression.

$x^{7} x + x^{7} \cdot - 3 + 5 x^{6} x + 5 x^{6} \cdot - 3 + 3 x^{5} x + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Simplify terms.

Simplify each term.

Multiply $x^{7}$ by $x$ by adding the exponents.

Multiply $x^{7}$ by $x$ .

Raise $x$ to the power of $1$ .

$x^{7} x^{1} + x^{7} \cdot - 3 + 5 x^{6} x + 5 x^{6} \cdot - 3 + 3 x^{5} x + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{7 + 1} + x^{7} \cdot - 3 + 5 x^{6} x + 5 x^{6} \cdot - 3 + 3 x^{5} x + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Add $7$ and $1$ .

$x^{8} + x^{7} \cdot - 3 + 5 x^{6} x + 5 x^{6} \cdot - 3 + 3 x^{5} x + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Move $- 3$ to the left of $x^{7}$ .

$x^{8} - 3 \cdot x^{7} + 5 x^{6} x + 5 x^{6} \cdot - 3 + 3 x^{5} x + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x^{6}$ by $x$ by adding the exponents.

Move $x$ .

$x^{8} - 3 x^{7} + 5 (x \cdot x^{6}) + 5 x^{6} \cdot - 3 + 3 x^{5} x + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x$ by $x^{6}$ .

Raise $x$ to the power of $1$ .

$x^{8} - 3 x^{7} + 5 (x^{1} x^{6}) + 5 x^{6} \cdot - 3 + 3 x^{5} x + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{8} - 3 x^{7} + 5 x^{1 + 6} + 5 x^{6} \cdot - 3 + 3 x^{5} x + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Add $1$ and $6$ .

$x^{8} - 3 x^{7} + 5 x^{7} + 5 x^{6} \cdot - 3 + 3 x^{5} x + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $- 3$ by $5$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{5} x + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x^{5}$ by $x$ by adding the exponents.

Move $x$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 (x \cdot x^{5}) + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x$ by $x^{5}$ .

Raise $x$ to the power of $1$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 (x^{1} x^{5}) + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{1 + 5} + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Add $1$ and $5$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} + 3 x^{5} \cdot - 3 - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $- 3$ by $3$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{4} x - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 (x \cdot x^{4}) - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x$ by $x^{4}$ .

Raise $x$ to the power of $1$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 (x^{1} x^{4}) - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{1 + 4} - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Add $1$ and $4$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} - 17 x^{4} \cdot - 3 - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $- 3$ by $- 17$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{3} x - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 (x \cdot x^{3}) - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 (x^{1} x^{3}) - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{1 + 3} - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Add $1$ and $3$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} - 16 x^{3} \cdot - 3 + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $- 3$ by $- 16$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{2} x + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 (x \cdot x^{2}) + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 (x^{1} x^{2}) + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{1 + 2} + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Add $1$ and $2$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{3} + 24 x^{2} \cdot - 3 + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $- 3$ by $24$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{3} - 72 x^{2} + 16 x \cdot x + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{3} - 72 x^{2} + 16 (x \cdot x) + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $x$ by $x$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{3} - 72 x^{2} + 16 x^{2} + 16 x \cdot - 3 - 16 x - 16 \cdot - 3$

Multiply $- 3$ by $16$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{3} - 72 x^{2} + 16 x^{2} - 48 x - 16 x - 16 \cdot - 3$

Multiply $- 16$ by $- 3$ .

$x^{8} - 3 x^{7} + 5 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{3} - 72 x^{2} + 16 x^{2} - 48 x - 16 x + 48$

Simplify by adding terms.

Add $- 3 x^{7}$ and $5 x^{7}$ .

$x^{8} + 2 x^{7} - 15 x^{6} + 3 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{3} - 72 x^{2} + 16 x^{2} - 48 x - 16 x + 48$

Add $- 15 x^{6}$ and $3 x^{6}$ .

$x^{8} + 2 x^{7} - 12 x^{6} - 9 x^{5} - 17 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{3} - 72 x^{2} + 16 x^{2} - 48 x - 16 x + 48$

Subtract $17 x^{5}$ from $- 9 x^{5}$ .

$x^{8} + 2 x^{7} - 12 x^{6} - 26 x^{5} + 51 x^{4} - 16 x^{4} + 48 x^{3} + 24 x^{3} - 72 x^{2} + 16 x^{2} - 48 x - 16 x + 48$

Subtract $16 x^{4}$ from $51 x^{4}$ .

$x^{8} + 2 x^{7} - 12 x^{6} - 26 x^{5} + 35 x^{4} + 48 x^{3} + 24 x^{3} - 72 x^{2} + 16 x^{2} - 48 x - 16 x + 48$

Add $48 x^{3}$ and $24 x^{3}$ .

$x^{8} + 2 x^{7} - 12 x^{6} - 26 x^{5} + 35 x^{4} + 72 x^{3} - 72 x^{2} + 16 x^{2} - 48 x - 16 x + 48$

Add $- 72 x^{2}$ and $16 x^{2}$ .

$x^{8} + 2 x^{7} - 12 x^{6} - 26 x^{5} + 35 x^{4} + 72 x^{3} - 56 x^{2} - 48 x - 16 x + 48$

Subtract $16 x$ from $- 48 x$ .

$x^{8} + 2 x^{7} - 12 x^{6} - 26 x^{5} + 35 x^{4} + 72 x^{3} - 56 x^{2} - 64 x + 48$

The largest exponent is the degree of the polynomial.

$8$

Find the Degree f(x)=(x+2)^4(x-1)^3(x-3)

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