Simplify (b^2+8)(b^2-8)

$(b^{2} + 8) (b^{2} - 8)$

Step 1

Expand $(b^{2} + 8) (b^{2} - 8)$ using the FOIL Method.

Apply the distributive property.

$b^{2} (b^{2} - 8) + 8 (b^{2} - 8)$

Apply the distributive property.

$b^{2} b^{2} + b^{2} \cdot - 8 + 8 (b^{2} - 8)$

Apply the distributive property.

$b^{2} b^{2} + b^{2} \cdot - 8 + 8 b^{2} + 8 \cdot - 8$

Step 2

Simplify terms.

Combine the opposite terms in $b^{2} b^{2} + b^{2} \cdot - 8 + 8 b^{2} + 8 \cdot - 8$ .

Reorder the factors in the terms $b^{2} \cdot - 8$ and $8 b^{2}$ .

$b^{2} b^{2} - 8 b^{2} + 8 b^{2} + 8 \cdot - 8$

Add $- 8 b^{2}$ and $8 b^{2}$ .

$b^{2} b^{2} + 0 + 8 \cdot - 8$

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

$b^{2} b^{2} + 8 \cdot - 8$

Simplify each term.

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

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

$b^{2 + 2} + 8 \cdot - 8$

Add $2$ and $2$ .

$b^{4} + 8 \cdot - 8$

Multiply $8$ by $- 8$ .

$b^{4} - 64$