Binomial Theorem Question 4
Question 4 - 2024 (27 Jan Shift 1)
If $A$ denotes the sum of all the coefficients in the expansion of $\left(1-3 x+10 x^{2}\right)^{n}$ and $B$ denotes the sum of all the coefficients in the expansion of $\left(1+x^{2}\right)^{n}$, then :
(1) $A=B^{3}$
(2) $3 \mathrm{~A}=\mathrm{B}$
(3) $B=A^{3}$
(4) $A=3 B$
Show Answer
Answer (1)
Solution
Sum of coefficients in the expansion of
$\left(1-3 x+10 x^{2}\right)^{n}=A$
then $A=(1-3+10)^{n}=8^{n}($ put $x=1)$
and sum of coefficients in the expansion of
$\left(1+x^{2}\right)^{n}=B$
then $B=(1+1)^{\mathrm{n}}=2^{\mathrm{n}}$
$\mathrm{A}=\mathrm{B}^{3}$
