Factor y^4-625

$y^{4} - 625$

Step 1

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

${(y^{2})}^{2} - 625$

Step 2

Rewrite $625$ as $25^{2}$ .

${(y^{2})}^{2} - 25^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y^{2}$ and $b = 25$ .

$(y^{2} + 25) (y^{2} - 25)$

Step 4

Simplify.

Rewrite $25$ as $5^{2}$ .

$(y^{2} + 25) (y^{2} - 5^{2})$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 5$ .

$(y^{2} + 25) ((y + 5) (y - 5))$

Remove unnecessary parentheses.

$(y^{2} + 25) (y + 5) (y - 5)$

Factor y^4-625

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