Factor x^10-x^7

$x^{10} - x^{7}$

Step 1

Factor $x^{7}$ out of $x^{10} - x^{7}$ .

Factor $x^{7}$ out of $x^{10}$ .

$x^{7} x^{3} - x^{7}$

Factor $x^{7}$ out of $- x^{7}$ .

$x^{7} x^{3} + x^{7} \cdot - 1$

Factor $x^{7}$ out of $x^{7} x^{3} + x^{7} \cdot - 1$ .

$x^{7} (x^{3} - 1)$

Step 2

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

$x^{7} (x^{3} - 1^{3})$

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 $b = 1$ .

$x^{7} ((x - 1) (x^{2} + x \cdot 1 + 1^{2}))$

Step 4

Factor.

Simplify.

Multiply $x$ by $1$ .

$x^{7} ((x - 1) (x^{2} + x + 1^{2}))$

One to any power is one.

$x^{7} ((x - 1) (x^{2} + x + 1))$

Remove unnecessary parentheses.

$x^{7} (x - 1) (x^{2} + x + 1)$

Factor x^10-x^7

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