Evaluate (x^2-1)^2

${(x^{2} - 1)}^{2}$

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

$(x^{2} - 1) (x^{2} - 1)$

Expand $(x^{2} - 1) (x^{2} - 1)$ using the FOIL Method.

Apply the distributive property.

$x^{2} (x^{2} - 1) - 1 (x^{2} - 1)$

Apply the distributive property.

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

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 1 - 1 x^{2} - 1 \cdot - 1$

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.

$x^{2 + 2} + x^{2} \cdot - 1 - 1 x^{2} - 1 \cdot - 1$

Add $2$ and $2$ .

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

Move $- 1$ to the left of $x^{2}$ .

$x^{4} - 1 \cdot x^{2} - 1 x^{2} - 1 \cdot - 1$

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$x^{4} - x^{2} - 1 x^{2} - 1 \cdot - 1$

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$x^{4} - x^{2} - x^{2} - 1 \cdot - 1$

Multiply $- 1$ by $- 1$ .

$x^{4} - x^{2} - x^{2} + 1$

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

$x^{4} - 2 x^{2} + 1$