Evaluate (x^2-2)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 2 - 2 x^{2} - 2 \cdot - 2$

Step 3

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.

$x^{2 + 2} + x^{2} \cdot - 2 - 2 x^{2} - 2 \cdot - 2$

Add $2$ and $2$ .

$x^{4} + x^{2} \cdot - 2 - 2 x^{2} - 2 \cdot - 2$

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

$x^{4} - 2 \cdot x^{2} - 2 x^{2} - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

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

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

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