Question

The number of dissimilar terms in the expansion of $(a+b+c{)}^{2n-1}-(a+b-c{)}^{2n+1}$ is

• A. $(n+1{)}^2$
• B. $(n-1{)}^2$
• C. $4n^2-1$
• D. none of these

Answer 1

Answer: (A)

$(n+1{)}^2$

Given

$(a+b+c{)}^{2n-1}-(a+b+c{)}^{2n+1}$

$=\left[\right(a+b{)}^{2n-1}+........+c^{2n-1}]-[(a+b{)}^{2n+1}+........+c^{2n+1}]$

Hence different terms is

$(2n+1)+(2n-1)+.....+3+1=\left(\frac{n+1}{2}\right)\cdot (2n+1+1)$

$=(n+1{)}^2$