Factor 5x^5-405x

$5 x^{5} - 405 x$

Step 1

Factor $5 x$ out of $5 x^{5} - 405 x$ .

Factor $5 x$ out of $5 x^{5}$ .

$5 x (x^{4}) - 405 x$

Factor $5 x$ out of $- 405 x$ .

$5 x (x^{4}) + 5 x (- 81)$

Factor $5 x$ out of $5 x (x^{4}) + 5 x (- 81)$ .

$5 x (x^{4} - 81)$

Step 2

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

$5 x ({(x^{2})}^{2} - 81)$

Step 3

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

$5 x ({(x^{2})}^{2} - 9^{2})$

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 $b = 9$ .

$5 x ((x^{2} + 9) (x^{2} - 9))$

Step 5

Factor.

Simplify.

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

$5 x ((x^{2} + 9) (x^{2} - 3^{2}))$

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 $b = 3$ .

$5 x ((x^{2} + 9) ((x + 3) (x - 3)))$

Remove unnecessary parentheses.

$5 x ((x^{2} + 9) (x + 3) (x - 3))$

Remove unnecessary parentheses.

$5 x (x^{2} + 9) (x + 3) (x - 3)$

Factor 5x^5-405x

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