Simplify (8a^2+4)(8a^2-4)

$(8 a^{2} + 4) (8 a^{2} - 4)$

Step 1

Expand $(8 a^{2} + 4) (8 a^{2} - 4)$ using the FOIL Method.

Apply the distributive property.

$8 a^{2} (8 a^{2} - 4) + 4 (8 a^{2} - 4)$

Apply the distributive property.

$8 a^{2} (8 a^{2}) + 8 a^{2} \cdot - 4 + 4 (8 a^{2} - 4)$

Apply the distributive property.

$8 a^{2} (8 a^{2}) + 8 a^{2} \cdot - 4 + 4 (8 a^{2}) + 4 \cdot - 4$

Step 2

Simplify terms.

Combine the opposite terms in $8 a^{2} (8 a^{2}) + 8 a^{2} \cdot - 4 + 4 (8 a^{2}) + 4 \cdot - 4$ .

Reorder the factors in the terms $8 a^{2} \cdot - 4$ and $4 (8 a^{2})$ .

$8 a^{2} (8 a^{2}) - 4 \cdot 8 a^{2} + 4 \cdot 8 a^{2} + 4 \cdot - 4$

Add $- 4 \cdot 8 a^{2}$ and $4 \cdot 8 a^{2}$ .

$8 a^{2} (8 a^{2}) + 0 + 4 \cdot - 4$

Add $8 a^{2} (8 a^{2})$ and $0$ .

$8 a^{2} (8 a^{2}) + 4 \cdot - 4$

Simplify each term.

Rewrite using the commutative property of multiplication.

$8 \cdot 8 a^{2} a^{2} + 4 \cdot - 4$

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

Move $a^{2}$ .

$8 \cdot 8 (a^{2} a^{2}) + 4 \cdot - 4$

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

$8 \cdot 8 a^{2 + 2} + 4 \cdot - 4$

Add $2$ and $2$ .

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

Multiply $8$ by $8$ .

$64 a^{4} + 4 \cdot - 4$

Multiply $4$ by $- 4$ .

$64 a^{4} - 16$