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Question

Mathematics Question on Binomial theorem

After simplification, what is the number of terms in the expansion of [(3x+y)5]4−[(3x−y)4]5[(3x + y)^5]^4 - [(3x-y)^4]^5 ?

A

4

B

5

C

10

D

11

Answer

10

Explanation

Solution

Given expression is : [(3x+y)5]4−[(3x−y)4]5=[(3x+y)]20−[(3x−y)]20[(3x + y)^5]^4 - [(3x - y)^4]^5 = [(3x + y)]^{20} - [(3x - y)]^{20} First and second expansion will have 21 terms each but odd terms in second expansion be Ist, 3rd, 5th,.....21st will be equal and opposite to those of first expansion. Thus, the number of terms in the expansion of above exapression is 10.