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

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

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

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $2$ .

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

Move $- 2$ to the left of $x^{2}$ .

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

Multiply $- 2$ by $- 2$ .

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

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

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

Apply the distributive property.

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

Simplify.

Multiply $- 4$ by $2$ .

$y = 2 x^{4} - 8 x^{2} + 2 \cdot 4$

Multiply $2$ by $4$ .

$y = 2 x^{4} - 8 x^{2} + 8$