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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot 1 - 1 x - 1 \cdot 1$ .

Reorder the factors in the terms $x \cdot 1$ and $- 1 x$ .

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

Subtract $1 x$ from $1 x$ .

$(x \cdot x + 0 - 1 \cdot 1) (4 x + 3) (x + 4)$

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $1$ .

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

Expand $(x^{2} - 1) (4 x + 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

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

Multiply $4$ by $- 1$ .

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

Multiply $- 1$ by $3$ .

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

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

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

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $3$ .

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

Multiply $4$ by $4$ .

$4 x^{4} + 16 x^{3} + 3 x^{2} x + 3 x^{2} \cdot 4 - 4 x \cdot x - 4 x \cdot 4 - 3 x - 3 \cdot 4$

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

Move $x$ .

$4 x^{4} + 16 x^{3} + 3 (x \cdot x^{2}) + 3 x^{2} \cdot 4 - 4 x \cdot x - 4 x \cdot 4 - 3 x - 3 \cdot 4$

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

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

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

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

$4 x^{4} + 16 x^{3} + 3 x^{1 + 2} + 3 x^{2} \cdot 4 - 4 x \cdot x - 4 x \cdot 4 - 3 x - 3 \cdot 4$

Add $1$ and $2$ .

$4 x^{4} + 16 x^{3} + 3 x^{3} + 3 x^{2} \cdot 4 - 4 x \cdot x - 4 x \cdot 4 - 3 x - 3 \cdot 4$

Multiply $4$ by $3$ .

$4 x^{4} + 16 x^{3} + 3 x^{3} + 12 x^{2} - 4 x \cdot x - 4 x \cdot 4 - 3 x - 3 \cdot 4$

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

Move $x$ .

$4 x^{4} + 16 x^{3} + 3 x^{3} + 12 x^{2} - 4 (x \cdot x) - 4 x \cdot 4 - 3 x - 3 \cdot 4$

Multiply $x$ by $x$ .

$4 x^{4} + 16 x^{3} + 3 x^{3} + 12 x^{2} - 4 x^{2} - 4 x \cdot 4 - 3 x - 3 \cdot 4$

Multiply $4$ by $- 4$ .

$4 x^{4} + 16 x^{3} + 3 x^{3} + 12 x^{2} - 4 x^{2} - 16 x - 3 x - 3 \cdot 4$

Multiply $- 3$ by $4$ .

$4 x^{4} + 16 x^{3} + 3 x^{3} + 12 x^{2} - 4 x^{2} - 16 x - 3 x - 12$

Simplify by adding terms.

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

$4 x^{4} + 19 x^{3} + 12 x^{2} - 4 x^{2} - 16 x - 3 x - 12$

Subtract $4 x^{2}$ from $12 x^{2}$ .

$4 x^{4} + 19 x^{3} + 8 x^{2} - 16 x - 3 x - 12$

Subtract $3 x$ from $- 16 x$ .

$4 x^{4} + 19 x^{3} + 8 x^{2} - 19 x - 12$

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

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