Simplify (a^2+b^2)(a^2-b^2)

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

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

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify terms.

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

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

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

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

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

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

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

Simplify each term.

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

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

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

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

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Move $b^{2}$ .

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

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

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

Add $2$ and $2$ .

$a^{4} - b^{4}$

Simplify (a^2+b^2)(a^2-b^2)

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