Simplify (x-4)(x^2+4x+16)

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $16$ to the left of $x$ .

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

Multiply $4$ by $- 4$ .

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

Multiply $- 4$ by $16$ .

$x^{3} + 4 x^{2} + 16 x - 4 x^{2} - 16 x - 64$

Combine the opposite terms in $x^{3} + 4 x^{2} + 16 x - 4 x^{2} - 16 x - 64$ .

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

$x^{3} + 16 x + 0 - 16 x - 64$

Add $x^{3} + 16 x$ and $0$ .

$x^{3} + 16 x - 16 x - 64$

Subtract $16 x$ from $16 x$ .

$x^{3} + 0 - 64$

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

$x^{3} - 64$