Calculus Examples

$9 a^{6} - 16 b^{8}$

Step 1

Rewrite $9 a^{6}$ as ${(3 a^{3})}^{2}$ .

${(3 a^{3})}^{2} - 16 b^{8}$

Step 2

Rewrite $16 b^{8}$ as ${(4 b^{4})}^{2}$ .

${(3 a^{3})}^{2} - {(4 b^{4})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 a^{3}$ and $b = 4 b^{4}$ .

$(3 a^{3} + 4 b^{4}) (3 a^{3} - (4 b^{4}))$

Step 4

Multiply $4$ by $- 1$ .

$(3 a^{3} + 4 b^{4}) (3 a^{3} - 4 b^{4})$