Evaluate (x+2)^2+4(x+2)+3

${(x + 2)}^{2} + 4 (x + 2) + 3$

Step 1

Simplify each term.

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

$(x + 2) (x + 2) + 4 (x + 2) + 3$

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

Apply the distributive property.

$x (x + 2) + 2 (x + 2) + 4 (x + 2) + 3$

Apply the distributive property.

$x \cdot x + x \cdot 2 + 2 (x + 2) + 4 (x + 2) + 3$

Apply the distributive property.

$x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2 + 4 (x + 2) + 3$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $2$ by $2$ .

$x^{2} + 2 x + 2 x + 4 + 4 (x + 2) + 3$

Add $2 x$ and $2 x$ .

$x^{2} + 4 x + 4 + 4 (x + 2) + 3$

Apply the distributive property.

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

Multiply $4$ by $2$ .

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

Step 2

Simplify by adding terms.

Add $4 x$ and $4 x$ .

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

Simplify by adding numbers.

Add $4$ and $8$ .

$x^{2} + 8 x + 12 + 3$

Add $12$ and $3$ .

$x^{2} + 8 x + 15$