Write in Standard Form -4(x-4)^2+16=0

$- 4 {(x - 4)}^{2} + 16 = 0$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 2

Simplify each term.

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

$- 4 ((x - 4) (x - 4)) + 16 = 0$

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

Apply the distributive property.

$- 4 (x (x - 4) - 4 (x - 4)) + 16 = 0$

Apply the distributive property.

$- 4 (x \cdot x + x \cdot - 4 - 4 (x - 4)) + 16 = 0$

Apply the distributive property.

$- 4 (x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4) + 16 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$- 4 (x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4) + 16 = 0$

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

$- 4 (x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4) + 16 = 0$

Multiply $- 4$ by $- 4$ .

$- 4 (x^{2} - 4 x - 4 x + 16) + 16 = 0$

Subtract $4 x$ from $- 4 x$ .

$- 4 (x^{2} - 8 x + 16) + 16 = 0$

Apply the distributive property.

$- 4 x^{2} - 4 (- 8 x) - 4 \cdot 16 + 16 = 0$

Simplify.

Multiply $- 8$ by $- 4$ .

$- 4 x^{2} + 32 x - 4 \cdot 16 + 16 = 0$

Multiply $- 4$ by $16$ .

$- 4 x^{2} + 32 x - 64 + 16 = 0$

Step 3

Add $- 64$ and $16$ .

$- 4 x^{2} + 32 x - 48 = 0$

Step 4