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  4. The sum of the co-efficients in the expansion of (1-2 x +5 x 2) n is ' a ' and the sum of the co-efficients in the expansion of (1+ x )2 n is b. Then -

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Q. The sum of the co-efficients in the expansion of $\left(1-2 x +5 x ^2\right)^{ n }$ is ' $a$ ' and the sum of the co-efficients in the expansion of $(1+ x )^{2 n }$ is $b$. Then -

Binomial Theorem

Solution:

$\left(1-2 x+5 x^2\right)^n$
For sum of coefficients put $x =1$
$\therefore a=(1-2+5)^n=4^n$
$(1+x)^{2 n}$
For sum of coefficients put $x =1$;
$ b =(1+ x )^{2 n }=2^{2 n }=\left(2^2\right)^{ n }=4^{ n }$
$\therefore a = b$