Write in Standard Form y=3(x+1)^2-3x^2

$y = 3 {(x + 1)}^{2} - 3 x^{2}$

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

Simplify the right side.

Simplify $3 {(x + 1)}^{2} - 3 x^{2}$ .

Simplify each term.

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$y = 3 ((x + 1) (x + 1)) - 3 x^{2}$

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$y = 3 (x (x + 1) + 1 (x + 1)) - 3 x^{2}$

Apply the distributive property.

$y = 3 (x \cdot x + x \cdot 1 + 1 (x + 1)) - 3 x^{2}$

Apply the distributive property.

$y = 3 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1) - 3 x^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = 3 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1) - 3 x^{2}$

Multiply $x$ by $1$ .

$y = 3 (x^{2} + x + 1 x + 1 \cdot 1) - 3 x^{2}$

Multiply $x$ by $1$ .

$y = 3 (x^{2} + x + x + 1 \cdot 1) - 3 x^{2}$

Multiply $1$ by $1$ .

$y = 3 (x^{2} + x + x + 1) - 3 x^{2}$

Add $x$ and $x$ .

$y = 3 (x^{2} + 2 x + 1) - 3 x^{2}$

Apply the distributive property.

$y = 3 x^{2} + 3 (2 x) + 3 \cdot 1 - 3 x^{2}$

Simplify.

Multiply $2$ by $3$ .

$y = 3 x^{2} + 6 x + 3 \cdot 1 - 3 x^{2}$

Multiply $3$ by $1$ .

$y = 3 x^{2} + 6 x + 3 - 3 x^{2}$

Combine the opposite terms in $3 x^{2} + 6 x + 3 - 3 x^{2}$ .

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

$y = 6 x + 3 + 0$

Add $6 x + 3$ and $0$ .

$y = 6 x + 3$

Rewrite the equation.

$6 x + 3 = y$

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

Subtract $y$ from both sides of the equation.

$6 x + 3 - y = 0$

Move $3$ .

$6 x - y + 3 = 0$

Subtract $3$ from both sides of the equation.

$6 x - y = - 3$

Write in Standard Form y=3(x+1)^2-3x^2

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