Simplify (x-2)(3x+4)(x+1)(x-3)

$(x - 2) (3 x + 4) (x + 1) (x - 3)$

Expand $(x - 2) (3 x + 4)$ using the FOIL Method.

Apply the distributive property.

$(x (3 x + 4) - 2 (3 x + 4)) (x + 1) (x - 3)$

Apply the distributive property.

$(x (3 x) + x \cdot 4 - 2 (3 x + 4)) (x + 1) (x - 3)$

Apply the distributive property.

$(x (3 x) + x \cdot 4 - 2 (3 x) - 2 \cdot 4) (x + 1) (x - 3)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$(3 x \cdot x + x \cdot 4 - 2 (3 x) - 2 \cdot 4) (x + 1) (x - 3)$

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

Move $x$ .

$(3 (x \cdot x) + x \cdot 4 - 2 (3 x) - 2 \cdot 4) (x + 1) (x - 3)$

Multiply $x$ by $x$ .

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

Move $4$ to the left of $x$ .

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

Multiply $3$ by $- 2$ .

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

Multiply $- 2$ by $4$ .

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

Subtract $6 x$ from $4 x$ .

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

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

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

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $3$ by $1$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $1$ .

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

Multiply $- 8$ by $1$ .

$(3 x^{3} + 3 x^{2} - 2 x^{2} - 2 x - 8 x - 8) (x - 3)$

Simplify by adding terms.

Subtract $2 x^{2}$ from $3 x^{2}$ .

$(3 x^{3} + x^{2} - 2 x - 8 x - 8) (x - 3)$

Subtract $8 x$ from $- 2 x$ .

$(3 x^{3} + x^{2} - 10 x - 8) (x - 3)$

Expand $(3 x^{3} + x^{2} - 10 x - 8) (x - 3)$ by multiplying each term in the first expression by each term in the second expression.

$3 x^{3} x + 3 x^{3} \cdot - 3 + x^{2} x + x^{2} \cdot - 3 - 10 x \cdot x - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

Simplify terms.

Simplify each term.

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

Move $x$ .

$3 (x \cdot x^{3}) + 3 x^{3} \cdot - 3 + x^{2} x + x^{2} \cdot - 3 - 10 x \cdot x - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

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

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

$3 (x^{1} x^{3}) + 3 x^{3} \cdot - 3 + x^{2} x + x^{2} \cdot - 3 - 10 x \cdot x - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

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

$3 x^{1 + 3} + 3 x^{3} \cdot - 3 + x^{2} x + x^{2} \cdot - 3 - 10 x \cdot x - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

Add $1$ and $3$ .

$3 x^{4} + 3 x^{3} \cdot - 3 + x^{2} x + x^{2} \cdot - 3 - 10 x \cdot x - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

Multiply $- 3$ by $3$ .

$3 x^{4} - 9 x^{3} + x^{2} x + x^{2} \cdot - 3 - 10 x \cdot x - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

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

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

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

$3 x^{4} - 9 x^{3} + x^{2} x^{1} + x^{2} \cdot - 3 - 10 x \cdot x - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

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

$3 x^{4} - 9 x^{3} + x^{2 + 1} + x^{2} \cdot - 3 - 10 x \cdot x - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

Add $2$ and $1$ .

$3 x^{4} - 9 x^{3} + x^{3} + x^{2} \cdot - 3 - 10 x \cdot x - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

Move $- 3$ to the left of $x^{2}$ .

$3 x^{4} - 9 x^{3} + x^{3} - 3 \cdot x^{2} - 10 x \cdot x - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

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

Move $x$ .

$3 x^{4} - 9 x^{3} + x^{3} - 3 x^{2} - 10 (x \cdot x) - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

Multiply $x$ by $x$ .

$3 x^{4} - 9 x^{3} + x^{3} - 3 x^{2} - 10 x^{2} - 10 x \cdot - 3 - 8 x - 8 \cdot - 3$

Multiply $- 3$ by $- 10$ .

$3 x^{4} - 9 x^{3} + x^{3} - 3 x^{2} - 10 x^{2} + 30 x - 8 x - 8 \cdot - 3$

Multiply $- 8$ by $- 3$ .

$3 x^{4} - 9 x^{3} + x^{3} - 3 x^{2} - 10 x^{2} + 30 x - 8 x + 24$

Simplify by adding terms.

Add $- 9 x^{3}$ and $x^{3}$ .

$3 x^{4} - 8 x^{3} - 3 x^{2} - 10 x^{2} + 30 x - 8 x + 24$

Subtract $10 x^{2}$ from $- 3 x^{2}$ .

$3 x^{4} - 8 x^{3} - 13 x^{2} + 30 x - 8 x + 24$

Subtract $8 x$ from $30 x$ .

$3 x^{4} - 8 x^{3} - 13 x^{2} + 22 x + 24$

Simplify (x-2)(3x+4)(x+1)(x-3)

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