Algebra Examples

$49 p^{12} - 9 q^{6}$

Step 1

Rewrite $49 p^{12}$ as ${(7 p^{6})}^{2}$ .

${(7 p^{6})}^{2} - 9 q^{6}$

Step 2

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

${(7 p^{6})}^{2} - {(3 q^{3})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7 p^{6}$ and $b = 3 q^{3}$ .

$(7 p^{6} + 3 q^{3}) (7 p^{6} - (3 q^{3}))$

Step 4

Multiply $3$ by $- 1$ .

$(7 p^{6} + 3 q^{3}) (7 p^{6} - 3 q^{3})$