Evaluate 3x^2+7x-(x+4)^2-9

$3 x^{2} + 7 x - {(x + 4)}^{2} - 9$

Step 1

Simplify each term.

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

$3 x^{2} + 7 x - ((x + 4) (x + 4)) - 9$

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

Apply the distributive property.

$3 x^{2} + 7 x - (x (x + 4) + 4 (x + 4)) - 9$

Apply the distributive property.

$3 x^{2} + 7 x - (x \cdot x + x \cdot 4 + 4 (x + 4)) - 9$

Apply the distributive property.

$3 x^{2} + 7 x - (x \cdot x + x \cdot 4 + 4 x + 4 \cdot 4) - 9$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$3 x^{2} + 7 x - (x^{2} + x \cdot 4 + 4 x + 4 \cdot 4) - 9$

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

$3 x^{2} + 7 x - (x^{2} + 4 \cdot x + 4 x + 4 \cdot 4) - 9$

Multiply $4$ by $4$ .

$3 x^{2} + 7 x - (x^{2} + 4 x + 4 x + 16) - 9$

Add $4 x$ and $4 x$ .

$3 x^{2} + 7 x - (x^{2} + 8 x + 16) - 9$

Apply the distributive property.

$3 x^{2} + 7 x - x^{2} - (8 x) - 1 \cdot 16 - 9$

Simplify.

Multiply $8$ by $- 1$ .

$3 x^{2} + 7 x - x^{2} - 8 x - 1 \cdot 16 - 9$

Multiply $- 1$ by $16$ .

$3 x^{2} + 7 x - x^{2} - 8 x - 16 - 9$

Step 2

Simplify by adding terms.

Subtract $x^{2}$ from $3 x^{2}$ .

$2 x^{2} + 7 x - 8 x - 16 - 9$

Subtract $8 x$ from $7 x$ .

$2 x^{2} - x - 16 - 9$

Subtract $9$ from $- 16$ .

$2 x^{2} - x - 25$