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Question

Which term in the expansion of (x3x2)10 is independent of x? Find its value.

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Solution

(x3x2)10
General formula of nth term of (a+b)m=mCn1am+1nbn1
Here, nth term =10Cn1(x)11n(3x2)n1(1)
As it is independent of n,
11n2=2(n1)
11n=4n4
15=5nn=3.
Putting n=3 os formula (1)
value =10c2(x)8(3)2(x2)2
=10×92×9
=5×81
=405

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