Question

If the sum of the coefficients in the expansion of ${(1-3x+10x^2)}^n$ is $a$ and if the sum of the coefficients in the expansion of ${(1+x^2)}^n$ is $b$, then

• A. $a=3b$
• B. $a=b^3$
• C. $b=a^3$
• D. $3a=b$

Answer 1

The correct option is B $a=b^3$

We have, $a=$ sum of the coefficients in the expansion of ${(1-3x+10x^2)}^n$
$=(1-3+10{)}^n=(8{)}^n=(2{)}^{3n}$
(by putting $x=1$)

Now, $b=$ sum of the coefficients in the expansion of ${(1+x^2)}^n$
$=(1+1{)}^n=2^n\text{Clearly},a=b^3$