Factorise: $x^{8} - x^{4} - 72$

({(x^{2})}^{2} + 3^{2}) (x^{4} + 8) = (x^{2} + 3) (x^{2} + 3) (x^{4} + 8)

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({(x^{2})}^{2} - 3^{2}) (x^{4} + 8) = (x^{2} + 7) (x^{2} + 3) (x^{4} + 8)

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({(x^{2})}^{2} - 3^{2}) (x^{4} + 3) = (x^{2} + 3) (x^{2} + 3) (x^{4} + 8)

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({(x^{2})}^{2} - 3^{2}) (x^{4} + 8) = (x^{2} + 3) (x^{2} + 3) (x^{4} + 8)

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Solution

The correct option is D $({(x^{2})}^{2} - 3^{2}) (x^{4} + 8) = (x^{2} + 3) (x^{2} + 3) (x^{4} + 8)$
Let $x^{4} = a$ . Then $x^{8} - x^{4} - 72 = a^{2} - a - 72$
$a^{2} - 9 a + 8 a - 72 = a (a - 9) + 8 (a - 9)$
$= (a - 9) (a + 8) = (x^{4} - 9) (x^{4} + 8)$
$= ({(x^{2})}^{2} - 3^{2}) (x^{4} + 8) = (x^{2} + 3) (x^{2} + 3) (x^{4} + 8)$

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