Find the product:
$(4 a^{2} + 2 b) (a^{2} b + a b)$

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Solution

Consider $(4 a^{2} + 2 b) (a^{2} b + a b)$

$(4 a^{2} + 2 b) (a^{2} b + a b) = 4 a^{2} (a^{2} b) + 4 a^{2} (a b) + 2 b (a^{2} b) + 2 b (a b)$

$= 4 a^{4} b + 4 a^{3} b + 2 a^{2} b^{2} + 2 a b^{2}$

$∴ (4 a^{2} + 2 b) (a^{2} b + a b) = 4 a^{4} b + 4 a^{3} b + 2 a^{2} b^{2} + 2 a b^{2}$

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