Factor 405x^4-5y^4

$405 x^{4} - 5 y^{4}$

Step 1

Factor $5$ out of $405 x^{4} - 5 y^{4}$ .

Factor $5$ out of $405 x^{4}$ .

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

Factor $5$ out of $- 5 y^{4}$ .

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

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

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

Step 2

Rewrite $81 x^{4}$ as ${(9 x^{2})}^{2}$ .

$5 ({(9 x^{2})}^{2} - y^{4})$

Step 3

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

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

Step 4

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

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

Step 5

Factor.

Simplify.

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

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

Factor.

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

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Factor 405x^4-5y^4

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