Find the Product (x^2+a^2)(x^2-a^2)

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify terms.

Combine the opposite terms in $x^{2} x^{2} + x^{2} (- a^{2}) + a^{2} x^{2} + a^{2} (- a^{2})$ .

Reorder the factors in the terms $x^{2} (- a^{2})$ and $a^{2} x^{2}$ .

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

Add $- a^{2} x^{2}$ and $a^{2} x^{2}$ .

$x^{2} x^{2} + 0 + a^{2} (- a^{2})$

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

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

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.

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

Add $2$ and $2$ .

$x^{4} + a^{2} (- a^{2})$

Rewrite using the commutative property of multiplication.

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

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

Move $a^{2}$ .

$x^{4} - (a^{2} a^{2})$

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

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

Add $2$ and $2$ .

$x^{4} - a^{4}$