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Question

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

A
27x3+9y3
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B
27x3
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Solution

The correct option is B 27x3
Substitute 2x3y=a and (x+3y)=b
(2x3y)3+(x+3y)3+3(2x3y)2(x+3y)+3(2x3y)(x+3y)2
=a3+b3+3a2b+3ab2
Now, on using the identity:
(a+b)3=a3+b3+3a2b+3ab2
=(a+b)3
=(2x3y+x+3y)3
=(3x)3
=27x3

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