Simplify $a^{2} (a^{2} - 2 a - 1) - a (a^{4} - 3 a^{3} + a)$

- a^{5} + 4 a^{4} - 2 a^{3}

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a^{5} + 4 a^{4} - 2 a^{3}

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- a^{5} + 4 a^{4} - 4 a^{3}

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- a^{5} - 4 a^{4} - 2 a^{3}

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Solution

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

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