A) \[{{({{x}^{2}}+{{a}^{2}})}^{n}}\]
B) \[{{({{x}^{2}}-{{a}^{2}})}^{n}}\]
C) \[{{(x-a)}^{2n}}\]
D) \[{{(x+a)}^{2n}}\]
Correct Answer: B
Solution :
\[{{(x+a)}^{n}}={{x}^{n}}+{{\,}^{n}}{{C}_{1}}{{x}^{n-1}}a{{+}^{{}}}\]..... \[=({{x}^{n}}+{{\,}^{n}}{{C}_{2}}{{x}^{n-2}}{{a}^{2}}+.......\]+\[{{(}^{n}}{{C}_{1}}{{x}^{n-1}}a+{{\,}^{n}}{{C}_{3}}{{x}^{n-3}}{{a}^{3}}+.....)\] =\[P+Q\] \[\therefore \] \[{{(x-a)}^{n}}=P-Q,\] As the terms are alter. +ve and -ve \[\therefore \] \[{{P}^{2}}-{{Q}^{2}}=(P+Q)(P-Q)={{(x+a)}^{n}}{{(x-a)}^{n}}\] \[{{P}^{2}}-{{Q}^{2}}={{({{x}^{2}}-{{a}^{2}})}^{n}}\]
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