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

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

Step 1

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

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

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 $1$ .

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $2$ to the left of $x$ .

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

Multiply $- 4$ by $4$ .

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

Multiply $4$ by $2$ .

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

Simplify by adding terms.

Combine the opposite terms in $x^{3} - 4 x^{2} + 2 x + 4 x^{2} - 16 x + 8$ .

Add $- 4 x^{2}$ and $4 x^{2}$ .

$x^{3} + 2 x + 0 - 16 x + 8$

Add $x^{3} + 2 x$ and $0$ .

$x^{3} + 2 x - 16 x + 8$

Subtract $16 x$ from $2 x$ .

$x^{3} - 14 x + 8$