Write the following cubes in the expanded form $(2 a + 3 b)^{3}$

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Solution

We know that $(x + y)^{3} = x^{3} + y^{3} + 3 x y (x + y)$
$(2 a + 3 b)^{3}$
Here x=2a and y=3b we get
$(2 a)^{3} + (3 b)^{3} + 3 (2 a) (3 b) (2 a + 3 b)$
= $8 a^{3} + 27 b^{3} + 18 a b (2 a + 3 b)$
= $8 a^{3} + 27 b^{3} + 36 a^{2} b + 54 a b^{2}$
= $8 a^{3} + 36 a^{2} b + 54 a b^{2} + 27 b^{3}$

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