Solve for a (x+2)^2=a

${(x + 2)}^{2} = a$

Step 1

Rewrite the equation as $a = {(x + 2)}^{2}$ .

$a = {(x + 2)}^{2}$

Step 2

Simplify ${(x + 2)}^{2}$ .

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

$a = (x + 2) (x + 2)$

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

Apply the distributive property.

$a = x (x + 2) + 2 (x + 2)$

Apply the distributive property.

$a = x \cdot x + x \cdot 2 + 2 (x + 2)$

Apply the distributive property.

$a = x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2$

$a = x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$a = x^{2} + x \cdot 2 + 2 x + 2 \cdot 2$

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

$a = x^{2} + 2 \cdot x + 2 x + 2 \cdot 2$

Multiply $2$ by $2$ .

$a = x^{2} + 2 x + 2 x + 4$

$a = x^{2} + 2 x + 2 x + 4$

Add $2 x$ and $2 x$ .

$a = x^{2} + 4 x + 4$

$a = x^{2} + 4 x + 4$

$a = x^{2} + 4 x + 4$

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