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  4. The total number of terms in the expansion of (x+a)100+(x-a)100 after simplification will be

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Q. The total number of terms in the expansion of $(x+a)^{100}+(x-a)^{100}$ after simplification will be

Binomial Theorem

Solution:

Since, $(a+b)^n+(a-b)^n$
$=2\left[{ }^n C_0 a^n b^0+{ }^n C_2 a^{n-2} b^2+{ }^n C_4 a^{n-4} b^4+\ldots\right] $
$ =2($ Sum of terms at odd places ) }
So,$(x+a)^{100}+(x-a)^{100}$
$=2\left({ }^{100} C_0 x^{100} a^0+{ }^{100} C_2 x^{98} a^2+\ldots .+{ }^{100} C_{100} a^{100}\right)$
$=51 $ terms