Simplify 2(x+2)^2-8

$2 {(x + 2)}^{2} - 8$

Step 1

Simplify each term.

Rewrite ${(x + 2)}^{2}$ as $(x + 2) (x + 2)$ .

$2 ((x + 2) (x + 2)) - 8$

Expand $(x + 2) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$2 (x (x + 2) + 2 (x + 2)) - 8$

Apply the distributive property.

$2 (x \cdot x + x \cdot 2 + 2 (x + 2)) - 8$

Apply the distributive property.

$2 (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) - 8$

$2 (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) - 8$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$2 (x^{2} + x \cdot 2 + 2 x + 2 \cdot 2) - 8$

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

$2 (x^{2} + 2 \cdot x + 2 x + 2 \cdot 2) - 8$

Multiply $2$ by $2$ .

$2 (x^{2} + 2 x + 2 x + 4) - 8$

$2 (x^{2} + 2 x + 2 x + 4) - 8$

Add $2 x$ and $2 x$ .

$2 (x^{2} + 4 x + 4) - 8$

$2 (x^{2} + 4 x + 4) - 8$

Apply the distributive property.

$2 x^{2} + 2 (4 x) + 2 \cdot 4 - 8$

Simplify.

Multiply $4$ by $2$ .

$2 x^{2} + 8 x + 2 \cdot 4 - 8$

Multiply $2$ by $4$ .

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

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

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

Step 2

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

Subtract $8$ from $8$ .

$2 x^{2} + 8 x + 0$

Add $2 x^{2} + 8 x$ and $0$ .

$2 x^{2} + 8 x$

$2 x^{2} + 8 x$

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