Question

If A and B are the sums of odd and even terms respectively in the expansion of $(x+a{)}^n$, then $(x+a{)}^{2n}-(x-a{)}^{2n}$ is equal to

• A. 4(A+B)
• B. 4(A-B)
• C. AB
• D. 4AB

Answer 1

The correct option is D

4AB

If A and B denote respectively the sums of odd terms and even terms in the expansion $(x+a{)}^n$

Then, $(x+a{)}^n=A+B....(1)$

$(x-a{)}^n=A-B.....(2)$

Squaring and subtracting equation (2)from (1) we get

$(x+a{)}^{2n}-(x-a^{2n})=(A+B{)}^2-(A-B{)}^2$

$\Rightarrow (x+a{)}^{2n}-(x-a{)}^{2n}=4AB$