Calculus Examples

$u^{3} - 64$

Step 1

Rewrite $64$ as $4^{3}$ .

$u^{3} - 4^{3}$

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 $a = u$ and $b = 4$ .

$(u - 4) (u^{2} + u \cdot 4 + 4^{2})$

Step 3

Simplify.

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Step 3.1

Move $4$ to the left of $u$ .

$(u - 4) (u^{2} + 4 u + 4^{2})$

Step 3.2

Raise $4$ to the power of $2$ .

$(u - 4) (u^{2} + 4 u + 16)$