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

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Solution

Given,

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

$= a \cdot 2 a^{2} + a (- 5 a b) + a \cdot 3 b^{2} + b \cdot 2 a^{2} + b (- 5 a b) + b \cdot 3 b^{2}$

$= 2 a^{2} a - 5 a a b + 3 a b^{2} + 2 a^{2} b - 5 a b b + 3 b^{2} b$

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

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