Factorise Completely : $625 - x^{4}$

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Solution

$625 - x^{4} = (25)^{2} - (x^{2})^{2} = (25 + x^{2}) (25 - x^{2}) = (25 + x^{2}) [(5)^{2} - (x)^{2}] = (25 + x^{2}) (5 + x) (5 - x)$

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x^{4} - 625

625 - x^{4}

(25 + x^{2}) (5 + x) (5 - x)

The factors of ( $x^{4} - 625)$ are

x^{4} + 4 y^{4}

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