Factor 256x^4-625y^4 - Math solver

$256 x^{4} - 625 y^{4}$

Rewrite $256 x^{4}$ as ${(16 x^{2})}^{2}$ .

${(16 x^{2})}^{2} - 625 y^{4}$

Rewrite $625 y^{4}$ as ${(25 y^{2})}^{2}$ .

${(16 x^{2})}^{2} - {(25 y^{2})}^{2}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 16 x^{2}$ and $b = 25 y^{2}$ .

$(16 x^{2} + 25 y^{2}) (16 x^{2} - (25 y^{2}))$

Simplify.

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Remove parentheses.

$(16 x^{2} + 25 y^{2}) (16 x^{2} - 1 \cdot 25 y^{2})$

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

$(16 x^{2} + 25 y^{2}) ({(4 x)}^{2} - 1 \cdot 25 y^{2})$

Rewrite $25 y^{2}$ as ${(5 y)}^{2}$ .

$(16 x^{2} + 25 y^{2}) ({(4 x)}^{2} - {(5 y)}^{2})$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 x$ and $b = 5 y$ .

$(16 x^{2} + 25 y^{2}) ((4 x + 5 y) (4 x - (5 y)))$

Factor.

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Multiply $5$ by $- 1$ .

$(16 x^{2} + 25 y^{2}) ((4 x + 5 y) (4 x - 5 y))$

Remove unnecessary parentheses.

$(16 x^{2} + 25 y^{2}) (4 x + 5 y) (4 x - 5 y)$

Factor 256x^4-625y^4

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