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

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

Expand $(x - 1) (x + 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $3$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Multiply $- 1$ by $3$ .

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

Subtract $x$ from $3 x$ .

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

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

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Move $- 1$ to the left of $x^{2}$ .

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

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $3$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $3$ by $- 3$ .

$(3 x^{3} - x^{2} + 6 x^{2} - 2 x - 9 x - 3 \cdot - 1) (x + 2)$

Multiply $- 3$ by $- 1$ .

$(3 x^{3} - x^{2} + 6 x^{2} - 2 x - 9 x + 3) (x + 2)$

Simplify by adding terms.

Add $- x^{2}$ and $6 x^{2}$ .

$(3 x^{3} + 5 x^{2} - 2 x - 9 x + 3) (x + 2)$

Subtract $9 x$ from $- 2 x$ .

$(3 x^{3} + 5 x^{2} - 11 x + 3) (x + 2)$

Expand $(3 x^{3} + 5 x^{2} - 11 x + 3) (x + 2)$ by multiplying each term in the first expression by each term in the second expression.

$3 x^{3} x + 3 x^{3} \cdot 2 + 5 x^{2} x + 5 x^{2} \cdot 2 - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

Simplify terms.

Simplify each term.

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

Move $x$ .

$3 (x \cdot x^{3}) + 3 x^{3} \cdot 2 + 5 x^{2} x + 5 x^{2} \cdot 2 - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

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

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

$3 (x^{1} x^{3}) + 3 x^{3} \cdot 2 + 5 x^{2} x + 5 x^{2} \cdot 2 - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

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

$3 x^{1 + 3} + 3 x^{3} \cdot 2 + 5 x^{2} x + 5 x^{2} \cdot 2 - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

Add $1$ and $3$ .

$3 x^{4} + 3 x^{3} \cdot 2 + 5 x^{2} x + 5 x^{2} \cdot 2 - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

Multiply $2$ by $3$ .

$3 x^{4} + 6 x^{3} + 5 x^{2} x + 5 x^{2} \cdot 2 - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

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

Move $x$ .

$3 x^{4} + 6 x^{3} + 5 (x \cdot x^{2}) + 5 x^{2} \cdot 2 - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

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

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

$3 x^{4} + 6 x^{3} + 5 (x^{1} x^{2}) + 5 x^{2} \cdot 2 - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

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

$3 x^{4} + 6 x^{3} + 5 x^{1 + 2} + 5 x^{2} \cdot 2 - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

Add $1$ and $2$ .

$3 x^{4} + 6 x^{3} + 5 x^{3} + 5 x^{2} \cdot 2 - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

Multiply $2$ by $5$ .

$3 x^{4} + 6 x^{3} + 5 x^{3} + 10 x^{2} - 11 x \cdot x - 11 x \cdot 2 + 3 x + 3 \cdot 2$

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

Move $x$ .

$3 x^{4} + 6 x^{3} + 5 x^{3} + 10 x^{2} - 11 (x \cdot x) - 11 x \cdot 2 + 3 x + 3 \cdot 2$

Multiply $x$ by $x$ .

$3 x^{4} + 6 x^{3} + 5 x^{3} + 10 x^{2} - 11 x^{2} - 11 x \cdot 2 + 3 x + 3 \cdot 2$

Multiply $2$ by $- 11$ .

$3 x^{4} + 6 x^{3} + 5 x^{3} + 10 x^{2} - 11 x^{2} - 22 x + 3 x + 3 \cdot 2$

Multiply $3$ by $2$ .

$3 x^{4} + 6 x^{3} + 5 x^{3} + 10 x^{2} - 11 x^{2} - 22 x + 3 x + 6$

Simplify by adding terms.

Add $6 x^{3}$ and $5 x^{3}$ .

$3 x^{4} + 11 x^{3} + 10 x^{2} - 11 x^{2} - 22 x + 3 x + 6$

Subtract $11 x^{2}$ from $10 x^{2}$ .

$3 x^{4} + 11 x^{3} - x^{2} - 22 x + 3 x + 6$

Add $- 22 x$ and $3 x$ .

$3 x^{4} + 11 x^{3} - x^{2} - 19 x + 6$

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

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