Algebra Examples

$49 x^{2} y^{6} z^{10} - a^{12}$

Step 1

Rewrite $49 x^{2} y^{6} z^{10}$ as ${(7 x y^{3} z^{5})}^{2}$ .

${(7 x y^{3} z^{5})}^{2} - a^{12}$

Step 2

Rewrite $a^{12}$ as ${(a^{6})}^{2}$ .

${(7 x y^{3} z^{5})}^{2} - {(a^{6})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7 x y^{3} z^{5}$ and $b = a^{6}$ .

$(7 x y^{3} z^{5} + a^{6}) (7 x y^{3} z^{5} - a^{6})$