When $a^{2} b (a^{3} - a + 1) - a b (a^{4} - 2 a^{2} + 2 a) - b (a^{3} - a^{2} - 1)$ is simplified, the answer is

- a^{2} b

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a b

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b

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0

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Solution

The correct option is C $b$
Given expression is,
$a^{2} b (a^{3} - a + 1) - a b (a^{4} - 2 a^{2} + 2 a) - b (a^{3} - a^{2} - 1)$
$= (a^{5} b - a^{3} b + a^{2} b) - (a^{5} b - 2 a^{3} b + 2 a^{2} b) - (a^{3} b - a^{2} b - b)$
$= a^{5} b - a^{3} b + a^{2} b - a^{5} b + 2 a^{3} b - 2 a^{2} b - a^{3} b + a^{2} b + b$
$= (a^{5} b - a^{5} b) + (2 a^{3} b - a^{3} b - a^{3} b) + (a^{2} b - 2 a^{2} b + a^{2} b) + b$
$= 0 + 0 + 0 + b$
$= b$
Option C is correct.

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