Simplify (x^2-1)(x^2+1)

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

Step 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.

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

Step 2

Simplify terms.

Combine the opposite terms in $x^{2} x^{2} + x^{2} \cdot 1 - 1 x^{2} - 1 \cdot 1$ .

Reorder the factors in the terms $x^{2} \cdot 1$ and $- 1 x^{2}$ .

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

Subtract $1 x^{2}$ from $1 x^{2}$ .

$x^{2} x^{2} + 0 - 1 \cdot 1$

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

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

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.

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

Add $2$ and $2$ .

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

Multiply $- 1$ by $1$ .

$x^{4} - 1$