Factorise $a^{2} (b + c) - (b + c)^{3}$

(b + c) (a^{2} - (b + c)^{2})

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(b - c) (a^{2} - (b + c)^{2})

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(b + c) (a^{2} + (b + c)^{2})

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None of these

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Solution

The correct option is C $(b + c) (a^{2} - (b + c)^{2})$
Solution:- (A) $(b + c) (a^{2} - {(b + c)}^{2})$
Let $b + c = x$ .
$∴ a^{2} (b + c) - {(b + c)}^{3} = a^{2} x - x^{3}$
$\Rightarrow = x (a^{2} - x^{2})$
$∵ x = b + c$
$∴ a^{2} (b + c) - {(b + c)}^{3} = (b + c) (a^{2} - {(b + c)}^{2})$

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