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)

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