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Question: The number of terms in the expansion of \(\lbrack(x + 3y)^{2}(3x - y)^{2}\rbrack^{3}\) is...

The number of terms in the expansion of [(x+3y)2(3x−y)2]3\lbrack(x + 3y)^{2}(3x - y)^{2}\rbrack^{3} is

A

14

B

28

C

32

D

56

Answer

28

Explanation

Solution

We have [(x+3y)(3x−y)]6\lbrack(x + 3y)(3x - y)\rbrack^{6}= [3x2+8xy−3y2]6\lbrack 3x^{2} + 8xy - 3y^{2}\rbrack^{6};

Number of terms = (6+1)(6+2)2=28\frac{(6 + 1)(6 + 2)}{2} = 28