Find the product of $(a + b)$ and $(2 a^{2} - 5 a b + 3 b^{2})$

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Solution

We need to find product of $(a + b)$ and $(2 a^{2} - 5 a b + 3 b^{2})$
$= (a + b) \times (2 a^{2} - 5 a b + 3 b^{2})$
$= a (2 a^{2} - 5 a b + 3 b^{2}) + b (2 a^{2} - 5 a b + 3 b^{2})$
$= 2 a^{3} - 5 a^{2} b + 3 a b^{2} + 2 a^{2} b - 5 a b^{2} + 3 b^{3}$
$= 2 a^{3} + 3 b^{3} - 2 a^{2} b - 2 a b^{2}$

Hence, the product of $(a + b)$ and $(2 a^{2} - 5 a b + 3 b^{2})$ is $2 a^{3} + 3 b^{3} - 2 a^{2} b - 2 a b^{2}$ .

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(a + b) (2 a^{2} - 5 a b + 3 b^{2})

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