Factor x^7-81x^3

$x^{7} - 81 x^{3}$

Step 1

Factor $x^{3}$ out of $x^{7} - 81 x^{3}$ .

Factor $x^{3}$ out of $x^{7}$ .

$x^{3} x^{4} - 81 x^{3}$

Factor $x^{3}$ out of $- 81 x^{3}$ .

$x^{3} x^{4} + x^{3} \cdot - 81$

Factor $x^{3}$ out of $x^{3} x^{4} + x^{3} \cdot - 81$ .

$x^{3} (x^{4} - 81)$

Step 2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$x^{3} ({(x^{2})}^{2} - 81)$

Step 3

Rewrite $81$ as $9^{2}$ .

$x^{3} ({(x^{2})}^{2} - 9^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = 9$ .

$x^{3} ((x^{2} + 9) (x^{2} - 9))$

Step 5

Factor.

Simplify.

Rewrite $9$ as $3^{2}$ .

$x^{3} ((x^{2} + 9) (x^{2} - 3^{2}))$

Factor.

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

$x^{3} ((x^{2} + 9) ((x + 3) (x - 3)))$

Remove unnecessary parentheses.

$x^{3} ((x^{2} + 9) (x + 3) (x - 3))$

Remove unnecessary parentheses.

$x^{3} (x^{2} + 9) (x + 3) (x - 3)$

Factor x^7-81x^3

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