First slide

Binomial theorem for positive integral Index

Question

In the expansion of ${(x + a)}^{n}$ , if the sum of odd terms be A and the sum of even terms be B, then value of ${(x^{2} - a^{2})}^{n}$ is

Moderate

A

AB
B

2AB
C

4AB
D

$A^{2} - B^{2}$

Solution

We have $(x + a)^{n} = A + B$ and $(x - a)^{n} = A - B$
$\begin{array}{l} ∴ {(x^{2} - a^{2})}^{n} = (x + a)^{n} (x - a)^{n} = (A + B) (A - B) \\ = A^{2} - B^{2} . \end{array}$

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