Question

$facorise 16 {a}^{3} - \frac{128}{ {b}^{3} }$
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Answer 1

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$factorise \: \: 16a {}^{ 3} - \frac{128}{b {}^{3} }$

$\:\:\:\: \: \: \: \: \: \: \: \: \: \: \large\mathfrak{\underline{\underline{\huge\mathcal{\bf{\boxed{\huge\mathcal{~~ANSWER~~}}}}}}}$

$\:\: \underline{\underline{\bf{\large\mathfrak{~~solution~~}}}}$

$16a {}^{3} - \frac{128}{b {}^{3} } \\ = 2(8a {}^{3} - \frac{64}{b {}^{3} } ) \\ = 2((2a) {}^{3} - (\frac{4}{b} ) {}^{3} ) \\ = 2(2a - \frac{4}{b} )(4a {}^{2} + \frac{16}{b {}^{2} } + 2a \times \frac{4}{b} ) \\ =2 (2a - \frac{4}{b} )(4a {}^{2} + \frac{16}{b {}^{2} } + \frac{8a}{b} )$