Find the Product (x^3+x^2+1)(x^2-x-5)

$(x^{3} + x^{2} + 1) (x^{2} - x - 5)$

Step 1

Expand $(x^{3} + x^{2} + 1) (x^{2} - x - 5)$ by multiplying each term in the first expression by each term in the second expression.

$x^{3} x^{2} + x^{3} (- x) + x^{3} \cdot - 5 + x^{2} x^{2} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

Step 2

Simplify terms.

Simplify each term.

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

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

$x^{3 + 2} + x^{3} (- x) + x^{3} \cdot - 5 + x^{2} x^{2} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

Add $3$ and $2$ .

$x^{5} + x^{3} (- x) + x^{3} \cdot - 5 + x^{2} x^{2} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

Rewrite using the commutative property of multiplication.

$x^{5} - x^{3} x + x^{3} \cdot - 5 + x^{2} x^{2} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

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

Move $x$ .

$x^{5} - (x \cdot x^{3}) + x^{3} \cdot - 5 + x^{2} x^{2} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

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

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

$x^{5} - (x^{1} x^{3}) + x^{3} \cdot - 5 + x^{2} x^{2} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

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

$x^{5} - x^{1 + 3} + x^{3} \cdot - 5 + x^{2} x^{2} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

Add $1$ and $3$ .

$x^{5} - x^{4} + x^{3} \cdot - 5 + x^{2} x^{2} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

Move $- 5$ to the left of $x^{3}$ .

$x^{5} - x^{4} - 5 \cdot x^{3} + x^{2} x^{2} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

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

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

$x^{5} - x^{4} - 5 x^{3} + x^{2 + 2} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

Add $2$ and $2$ .

$x^{5} - x^{4} - 5 x^{3} + x^{4} + x^{2} (- x) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

Rewrite using the commutative property of multiplication.

$x^{5} - x^{4} - 5 x^{3} + x^{4} - x^{2} x + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

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

Move $x$ .

$x^{5} - x^{4} - 5 x^{3} + x^{4} - (x \cdot x^{2}) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

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

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

$x^{5} - x^{4} - 5 x^{3} + x^{4} - (x^{1} x^{2}) + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

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

$x^{5} - x^{4} - 5 x^{3} + x^{4} - x^{1 + 2} + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

Add $1$ and $2$ .

$x^{5} - x^{4} - 5 x^{3} + x^{4} - x^{3} + x^{2} \cdot - 5 + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

Move $- 5$ to the left of $x^{2}$ .

$x^{5} - x^{4} - 5 x^{3} + x^{4} - x^{3} - 5 \cdot x^{2} + 1 x^{2} + 1 (- x) + 1 \cdot - 5$

Multiply $x^{2}$ by $1$ .

$x^{5} - x^{4} - 5 x^{3} + x^{4} - x^{3} - 5 x^{2} + x^{2} + 1 (- x) + 1 \cdot - 5$

Multiply $- x$ by $1$ .

$x^{5} - x^{4} - 5 x^{3} + x^{4} - x^{3} - 5 x^{2} + x^{2} - x + 1 \cdot - 5$

Multiply $- 5$ by $1$ .

$x^{5} - x^{4} - 5 x^{3} + x^{4} - x^{3} - 5 x^{2} + x^{2} - x - 5$

Simplify by adding terms.

Combine the opposite terms in $x^{5} - x^{4} - 5 x^{3} + x^{4} - x^{3} - 5 x^{2} + x^{2} - x - 5$ .

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

$x^{5} - 5 x^{3} + 0 - x^{3} - 5 x^{2} + x^{2} - x - 5$

Add $x^{5} - 5 x^{3}$ and $0$ .

$x^{5} - 5 x^{3} - x^{3} - 5 x^{2} + x^{2} - x - 5$

Subtract $x^{3}$ from $- 5 x^{3}$ .

$x^{5} - 6 x^{3} - 5 x^{2} + x^{2} - x - 5$

Add $- 5 x^{2}$ and $x^{2}$ .

$x^{5} - 6 x^{3} - 4 x^{2} - x - 5$

Find the Product (x^3+x^2+1)(x^2-x-5)

Related Questions

Support LCMGCF.com by disabling your adblocker.