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

Question

Aicharya · Accepted Answer

Solution: If A and B denote respectively the sums of odd terms and even terms in the expansion $(\text{x}+\text{a})^{\text{n}}.$ Then, $(\text{x}+\text{a})^{\text{n}}=\text{A}+\text{B}\ ...(\text{i})$ $(\text{x}-\text{a})^{\text{n}}=\text{A}-\text{B}\ ...(\text{ii})$ Multplying both the equations we get, $(\text{x}+\text{a})^{\text{n}}(\text{x}-\text{a})^{\text{n}}=\text{A}^{2}-\text{B}^{2}$ $\Rightarrow (\text{x}-\text{a})^{\text{n}}=\text{A}^{2}-\text{B}^{2}$

If the sum of odd numbered terms and the sum of even numbered terms in the expansion of…

Solution