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Question

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

A
72x2y+54y3
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B
54x2y+72y3
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C
72x2y
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D
54x2y
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Solution

The correct option is A 72x2y+54y3
Given,
(2x+3y)3(2x3y)3.
This is of the form (a3b3)=(ab)(a2+ab+b2), [Here a = (2x+3y)3, b = (2x3y)3]

Applying the identity,
(2x+3y)3(2x3y)3
=[(2x+3y)(2x3y)][(2x+3y)2+(2x+3y)(2x3y)+(2x3y)2]
=[2x+3y2x+3y][4x2+12xy+9y2+4x29y2+4x212xy+9y2]
=6y(12x2+9y2)
=72x2y+54y3

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