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UPSC NDA Math Model Paper 8

Question : 100 of 120

Marks: +1, -0

[(a+b)^{2}+(a-b)^{2}]^{2}

are

Solution:

We have to find number of terms in the expansion of

[(a+b)^{2}+(a-b)^{2}]^{2}

\Rightarrow[(a+b)^{2}+(a-b)^{2}]^{2}

=(a^{2}+2 a b+b^{2}+a^{2}-2 a b+b^{2})^{2}

=[2(a^{2}+b^{2})]^{2}

=4(a^{2}+b^{2})^{2}

As we know the total number of terms in the expansion of

(x+y)^{n}

n+1

Here

n=2

Therefore, total number of terms is

2+1=3

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