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

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

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

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

Simplify each term.

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

$y = 2 ((x + 1) (x + 1)) - 2$

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

Apply the distributive property.

$y = 2 (x (x + 1) + 1 (x + 1)) - 2$

Apply the distributive property.

$y = 2 (x \cdot x + x \cdot 1 + 1 (x + 1)) - 2$

Apply the distributive property.

$y = 2 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1) - 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $x$ by $1$ .

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

Multiply $1$ by $1$ .

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

Add $x$ and $x$ .

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

Apply the distributive property.

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

Simplify.

Multiply $2$ by $2$ .

$y = 2 x^{2} + 4 x + 2 \cdot 1 - 2$

Multiply $2$ by $1$ .

$y = 2 x^{2} + 4 x + 2 - 2$

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

Subtract $2$ from $2$ .

$y = 2 x^{2} + 4 x + 0$

Add $2 x^{2} + 4 x$ and $0$ .

$y = 2 x^{2} + 4 x$