Sum of
$(3 a^{2} b - 2 b^{2} a + a b - 3)$ and $(a^{3} - a b + 2 b^{2} a + 9)$
is .

a^{3} - 3 a^{2} b + 6

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a^{3} + 3 a^{2} b + 6

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2 a^{3} + 3 a^{2} b - 6

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2 a^{3} - 3 a^{2} b - 6

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Solution

The correct option is B $a^{3} + 3 a^{2} b + 6$
Given:
$= (3 a^{2} b - 2 b^{2} a + a b - 3)$
$+ (a^{3} - a b + 2 b^{2} a + 9)$
Grouping the like terms together, we get,
$= (a^{3}) + (3 a^{2} b) + (- 2 b^{2} a + 2 b^{2} a) + (- 3 + 9)$
$= a^{3} + 3 a^{2} b + 6$

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