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Simplify: $(a + b) (a^{2} + a b + 1)$

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$a^{3} + a b + a b^{2} + a$

$2 a^{2} b + 2 b^{2} + a + b$

$a^{3} + 2 a^{2} b + a b^{2} + a + b$

$a^{2} + a b + b^{2}$

answer is A.

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Detailed Solution

$(a + b) (a^{2} + a b + 1)$

$= a (a^{2} + a b + 1) + b (a^{2} + a b + 1)$

$= a^{3} + a^{2} b + a + a^{2} b + a b^{2} + b$

Collecting the like terms together, we get

$= a^{3} + a^{2} b + a^{2} b + a b^{2} + a + b$

$= a^{3} + 2 a^{2} b + a b^{2} + a + b$

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