Algebra Examples

$a^{6} - b^{2} x^{8}$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Remove parentheses.

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