Algebra Examples

$a^{2 x + 6} - 9 b^{6 y}$

Step 1

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

${(a^{x + 3})}^{2} - 9 b^{6 y}$

Step 2

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

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

Step 3

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

$(a^{x + 3} + 3 b^{3 y}) (a^{x + 3} - (3 b^{3 y}))$

Step 4

Multiply $3$ by $- 1$ .

$(a^{x + 3} + 3 b^{3 y}) (a^{x + 3} - 3 b^{3 y})$