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

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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, $(\text{x}+\text{a})^{\text{n}}=\text{A}+\text{B}\ ...(\text{i})$ $(\text{x}-\text{a})^{\text{n}}=\text{A}-\text{B}\ ...(\text{ii})$ Squaring and subtraction equation (ii) from(i) we get, $ (\text{x}+\text{a})^{2\text{n}}-(\text{x}-\text{a})^{2\text{n}}=(\text{A}+\text{B})^{2}-(\text{A}-\text{B})^{2}$ $\Rightarrow (\text{x}+\text{a})^{2\text{n}}-(\text{x}-\text{a})^{2\text{n}}=4\text{AB}$

If A and B are the sums of odd and even terms respectively in the expansion of…

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