Find the Product (a^3-b^2)(a^3+b^2)

$(a^{3} - b^{2}) (a^{3} + b^{2})$

Expand $(a^{3} - b^{2}) (a^{3} + b^{2})$ using the FOIL Method.

Apply the distributive property.

$a^{3} (a^{3} + b^{2}) - b^{2} (a^{3} + b^{2})$

Apply the distributive property.

$a^{3} a^{3} + a^{3} b^{2} - b^{2} (a^{3} + b^{2})$

Apply the distributive property.

$a^{3} a^{3} + a^{3} b^{2} - b^{2} a^{3} - b^{2} b^{2}$

Simplify terms.

Combine the opposite terms in $a^{3} a^{3} + a^{3} b^{2} - b^{2} a^{3} - b^{2} b^{2}$ .

Reorder the factors in the terms $a^{3} b^{2}$ and $- b^{2} a^{3}$ .

$a^{3} a^{3} + a^{3} b^{2} - a^{3} b^{2} - b^{2} b^{2}$

Subtract $a^{3} b^{2}$ from $a^{3} b^{2}$ .

$a^{3} a^{3} + 0 - b^{2} b^{2}$

Add $a^{3} a^{3}$ and $0$ .

$a^{3} a^{3} - b^{2} b^{2}$

Simplify each term.

Multiply $a^{3}$ by $a^{3}$ by adding the exponents.

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

$a^{3 + 3} - b^{2} b^{2}$

Add $3$ and $3$ .

$a^{6} - b^{2} b^{2}$

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

Move $b^{2}$ .

$a^{6} - (b^{2} b^{2})$

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

$a^{6} - b^{2 + 2}$

Add $2$ and $2$ .

$a^{6} - b^{4}$