Question

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

• A. $A^2-B^2$
• B. $A^2+B^2$
• C. 4AB
• D. None of these

Answer 1

The correct option is A

$A^2-B^2$

$A^2-B^2$

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

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

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

Multiplying both the equations we get

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

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