Simplify 2(x+4)^2-7(x+4)-4

$2 {(x + 4)}^{2} - 7 (x + 4) - 4$

Step 1

Simplify each term.

Rewrite ${(x + 4)}^{2}$ as $(x + 4) (x + 4)$ .

$2 ((x + 4) (x + 4)) - 7 (x + 4) - 4$

Expand $(x + 4) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$2 (x (x + 4) + 4 (x + 4)) - 7 (x + 4) - 4$

Apply the distributive property.

$2 (x \cdot x + x \cdot 4 + 4 (x + 4)) - 7 (x + 4) - 4$

Apply the distributive property.

$2 (x \cdot x + x \cdot 4 + 4 x + 4 \cdot 4) - 7 (x + 4) - 4$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$2 (x^{2} + x \cdot 4 + 4 x + 4 \cdot 4) - 7 (x + 4) - 4$

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

$2 (x^{2} + 4 \cdot x + 4 x + 4 \cdot 4) - 7 (x + 4) - 4$

Multiply $4$ by $4$ .

$2 (x^{2} + 4 x + 4 x + 16) - 7 (x + 4) - 4$

Add $4 x$ and $4 x$ .

$2 (x^{2} + 8 x + 16) - 7 (x + 4) - 4$

Apply the distributive property.

$2 x^{2} + 2 (8 x) + 2 \cdot 16 - 7 (x + 4) - 4$

Simplify.

Multiply $8$ by $2$ .

$2 x^{2} + 16 x + 2 \cdot 16 - 7 (x + 4) - 4$

Multiply $2$ by $16$ .

$2 x^{2} + 16 x + 32 - 7 (x + 4) - 4$

Apply the distributive property.

$2 x^{2} + 16 x + 32 - 7 x - 7 \cdot 4 - 4$

Multiply $- 7$ by $4$ .

$2 x^{2} + 16 x + 32 - 7 x - 28 - 4$

Step 2

Simplify by adding terms.

Subtract $7 x$ from $16 x$ .

$2 x^{2} + 9 x + 32 - 28 - 4$

Subtract $28$ from $32$ .

$2 x^{2} + 9 x + 4 - 4$

Combine the opposite terms in $2 x^{2} + 9 x + 4 - 4$ .

Subtract $4$ from $4$ .

$2 x^{2} + 9 x + 0$

Add $2 x^{2} + 9 x$ and $0$ .

$2 x^{2} + 9 x$