Find the Product (x^2-4x+16)(x+4)

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

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

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

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $2$ and $1$ .

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

Move $4$ to the left of $x^{2}$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $- 4$ .

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

Multiply $16$ by $4$ .

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

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

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

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

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

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

Add $- 16 x$ and $16 x$ .

$x^{3} + 0 + 64$

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

$x^{3} + 64$