Find the Product (a^6+7)(a^6-9)

$(a^{6} + 7) (a^{6} - 9)$

Step 1

Expand $(a^{6} + 7) (a^{6} - 9)$ using the FOIL Method.

Apply the distributive property.

$a^{6} (a^{6} - 9) + 7 (a^{6} - 9)$

Apply the distributive property.

$a^{6} a^{6} + a^{6} \cdot - 9 + 7 (a^{6} - 9)$

Apply the distributive property.

$a^{6} a^{6} + a^{6} \cdot - 9 + 7 a^{6} + 7 \cdot - 9$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $a^{6}$ by $a^{6}$ by adding the exponents.

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

$a^{6 + 6} + a^{6} \cdot - 9 + 7 a^{6} + 7 \cdot - 9$

Add $6$ and $6$ .

$a^{12} + a^{6} \cdot - 9 + 7 a^{6} + 7 \cdot - 9$

Move $- 9$ to the left of $a^{6}$ .

$a^{12} - 9 \cdot a^{6} + 7 a^{6} + 7 \cdot - 9$

Multiply $7$ by $- 9$ .

$a^{12} - 9 a^{6} + 7 a^{6} - 63$

Add $- 9 a^{6}$ and $7 a^{6}$ .

$a^{12} - 2 a^{6} - 63$