The factors of $625 a^{12} - 81 b^{12}$ are:

(25 a^{6} + 9 b^{6}) (5 a^{3} - 3 b^{3}) (5 a^{3} + 3 b^{3})

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{(5 a^{3} + 3 b^{3})}^{2} {(5 a^{3} - 3 b^{3})}^{2}

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{(5 a^{3} - 3 b^{3})}^{4}

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{(25 a^{6} - 9 b^{6})}^{2}

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Solution

The correct option is A $(25 a^{6} + 9 b^{6}) (5 a^{3} - 3 b^{3}) (5 a^{3} + 3 b^{3})$
$625 a^{12} - 8 b^{12}$
$= {({25 a}^{6})}^{2} - {({9 b}^{6})}^{2} = ({25 a}^{6} - {9 b}^{6}) ({25 a}^{6} + {9 b}^{6})$
$= [{({5 a}^{3})}^{2} - {({3 b}^{3})}^{2}] ({25 a}^{6} + {9 b}^{6})$
$= ({5 a}^{3} - {3 b}^{3}) ({5 a}^{3} + {3 b}^{3}) ({25 a}^{6} + {9 b}^{6})$

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