Calculus Examples

$(x^{3} - 8)$

Step 1

Remove parentheses.

$x^{3} - 8$

Step 2

Rewrite $8$ as $2^{3}$ .

$x^{3} - 2^{3}$

Step 3

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 $a = x$ and $b = 2$ .

$(x - 2) (x^{2} + x \cdot 2 + 2^{2})$

Step 4

Simplify.

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Step 4.1

Move $2$ to the left of $x$ .

$(x - 2) (x^{2} + 2 x + 2^{2})$

Step 4.2

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

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