A) \[{{P}^{2}}+{{Q}^{2}}\]
B) \[4PQ\]
C) \[{{P}^{2}}-{{Q}^{2}}\]
D) \[2P-2Q\]
Correct Answer: C
Solution :
Since, in the expansion of\[{{(x+a)}^{n}},\]sum of odd terms is P and sum of even terms is Q. So,\[P+Q\]is the sum of total terms in this expansion. Similarly,\[P-Q\] is the sum of total terms in the expansion of\[{{(x-a)}^{n}}\]. \[\therefore \] \[P+Q={{(x+a)}^{n}}\] and \[P-Q={{(x-a)}^{n}}\] \[\therefore \] \[{{(x+a)}^{n}}{{(x-a)}^{n}}=(P+Q)(P-Q)\] \[\Rightarrow \] \[{{({{x}^{2}}-{{a}^{2}})}^{n}}={{P}^{2}}-{{Q}^{2}}\]
You need to login to perform this action.
You will be redirected in
3 sec
