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

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

Step 1

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

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

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 $1$ .

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $4$ to the left of $x$ .

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

Multiply $2$ by $- 2$ .

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

Multiply $- 2$ by $4$ .

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

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

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

$x^{3} + 4 x + 0 - 4 x - 8$

Add $x^{3} + 4 x$ and $0$ .

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

Subtract $4 x$ from $4 x$ .

$x^{3} + 0 - 8$

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

$x^{3} - 8$