Write in Standard Form y=6x^2-6(x-2)^2

$y = 6 x^{2} - 6 {(x - 2)}^{2}$

The standard form of a linear equation is $A x + B y = C$ .

Simplify the right side.

Simplify $6 x^{2} - 6 {(x - 2)}^{2}$ .

Simplify each term.

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

$y = 6 x^{2} - 6 ((x - 2) (x - 2))$

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

Apply the distributive property.

$y = 6 x^{2} - 6 (x (x - 2) - 2 (x - 2))$

Apply the distributive property.

$y = 6 x^{2} - 6 (x \cdot x + x \cdot - 2 - 2 (x - 2))$

Apply the distributive property.

$y = 6 x^{2} - 6 (x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = 6 x^{2} - 6 (x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2)$

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

$y = 6 x^{2} - 6 (x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2)$

Multiply $- 2$ by $- 2$ .

$y = 6 x^{2} - 6 (x^{2} - 2 x - 2 x + 4)$

Subtract $2 x$ from $- 2 x$ .

$y = 6 x^{2} - 6 (x^{2} - 4 x + 4)$

Apply the distributive property.

$y = 6 x^{2} - 6 x^{2} - 6 (- 4 x) - 6 \cdot 4$

Simplify.

Multiply $- 4$ by $- 6$ .

$y = 6 x^{2} - 6 x^{2} + 24 x - 6 \cdot 4$

Multiply $- 6$ by $4$ .

$y = 6 x^{2} - 6 x^{2} + 24 x - 24$

Simplify by adding terms.

Subtract $6 x^{2}$ from $6 x^{2}$ .

$y = 0 + 24 x - 24$

Add $0$ and $24 x$ .

$y = 24 x - 24$

Rewrite the equation.

$24 x - 24 = y$

Move all terms containing variables to the left side of the equation.

Subtract $y$ from both sides of the equation.

$24 x - 24 - y = 0$

Move $- 24$ .

$24 x - y - 24 = 0$

Add $24$ to both sides of the equation.

$24 x - y = 24$