Question

The total number of terms in the expansion of ${(x+a)^{47} - (x-a)^{47}}$ after simplification is

• A. 24
• B. 47
• C. 48
• D. 96

Answer 1

Answer: (A)

24

Answer 2

Total number of terms in $(x+a)^{n}-(x-a)^{n}$
$=\begin{cases}\frac{n+1}{2} & \text { if } n \text { is odd } \\\ \frac{n}{2} & \text { if } n \text { is even }\end{cases}$
$\therefore$ Total number of terms in the expansion of
$(x+a)^{47}-(x-a)^{47}=\frac{47+1}{2} [\because n$ is odd $]$
$=\frac{48}{2}$
$=24$