Factorisation of the expression : $225 x^{5} - 256 x^{3}$ results in

x (15 x - 16) (15 x + 16)

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x^{2} (15 x + 16) (15 x - 16)

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(15 x - 16) (15 x + 16)

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x^{3} (15 x - 16) (15 x + 16)

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Solution

The correct option is C $x^{3} (15 x - 16) (15 x + 16)$
$225 x^{5} - 256 x^{3} = x^{3} (225 x^{2} - 256)$
$= x^{3} [{(15 x)}^{2} - {(16)}^{2}]$
$= x^{3} (15 x - 16) (15 x + 16)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

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