Precalculus Examples

$a^{6} - b^{3}$

Step 1

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

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

Step 2

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

$(a^{2} - b) ({(a^{2})}^{2} + a^{2} b + b^{2})$

Step 3

Multiply the exponents in ${(a^{2})}^{2}$ .

Tap for more steps...

Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$(a^{2} - b) (a^{2 \cdot 2} + a^{2} b + b^{2})$

Step 3.2

Multiply $2$ by $2$ .

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