Find the cube of $(3 a + 5 b)$

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Solution

Cube of $3 a + 5 b = (3 a + 5 b)^{3}$
Using, $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$= (3 a)^{3} + (5 b)^{3} + 3 (3 a) (5 b) (3 a + 5 b)$
$= 27 a^{3} + 125 b^{3} + 45 a b (3 a + 5 b)$
$= 27 a^{3} + 125 b^{3} + 135 a^{2} b + 225 a b^{2}$

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