The value of (2x−3y)3+(x+3y)3+3(2x−3y)2(x+3y)+3(2x−3y)(x+3y

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Question

The value of

(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2} =

Options:

A . 27x3

B . 29x3+(x+3y)3

C . (2x−3y)3+(x+3y)3

D . 0

Answer: Option A
:
A
Substitute

2 x - 3 y = a

and

(x + 3 y) = b

(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2}

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

= (a + b)^{3}

= (2 x - 3 y + x + 3 y)^{3}

= (3 x)^{3}

= 27 x^{3}

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