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  4. If ' a ' be the sum of the odd terms ' b ' be the sum of the even terms in the expansion of (1+ x ) n , then (1-x)n is equal to -

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Q. If ' $a$ ' be the sum of the odd terms & ' $b$ ' be the sum of the even terms in the expansion of $(1+ x )^{ n }$, then $(1-x)^n$ is equal to -

Binomial Theorem

Solution:

Given $(1+ x )^{ n }= a + b \ldots \ldots(1)$
then, $(1- x )^{ n }= a - b \ldots \ldots(2)$
Multiplying equation (1) & (2)
we get, $\left(1- x ^2\right)^{ n }= a ^2- b ^2$