Precalculus Examples

$x^{12} - x^{9}$

Step 1

Factor $x^{9}$ out of $x^{12} - x^{9}$ .

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Step 1.1

Factor $x^{9}$ out of $x^{12}$ .

$x^{9} x^{3} - x^{9}$

Step 1.2

Factor $x^{9}$ out of $- x^{9}$ .

$x^{9} x^{3} + x^{9} \cdot - 1$

Step 1.3

Factor $x^{9}$ out of $x^{9} x^{3} + x^{9} \cdot - 1$ .

$x^{9} (x^{3} - 1)$

Step 2

Rewrite $1$ as $1^{3}$ .

$x^{9} (x^{3} - 1^{3})$

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 $b = 1$ .

$x^{9} ((x - 1) (x^{2} + x \cdot 1 + 1^{2}))$

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Multiply $x$ by $1$ .

$x^{9} ((x - 1) (x^{2} + x + 1^{2}))$

Step 4.1.2

One to any power is one.

$x^{9} ((x - 1) (x^{2} + x + 1))$

Step 4.2

Remove unnecessary parentheses.

$x^{9} (x - 1) (x^{2} + x + 1)$