$a ({5 a}^{2} - 4 a - 3) - a^{2} (4 a - 1) + a (1 - {2 a}^{2})$ when simplified equals

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{2 a}^{2}

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- a^{3} - {3 a}^{2} - 2 a

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a^{3} - 2 a

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Solution

The correct option is D $- a^{3} - {3 a}^{2} - 2 a$
Given, $a (5 a^{2} - 4 a - 3) - a^{2} (4 a - 1) + a (1 - 2 a^{2})$
$=$ $5 a^{3} - 4 a^{2} - 3 a - 4 a^{3} + a^{2} + a - 2 a^{3}$
$=$ $(5 a^{3} - 4 a^{3} - 2 a^{3}) + (- 4 a^{2} + a^{2}) + (- 3 a + a)$
$=$ $- a^{3} - 3 a^{2} - 2 a$

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