Question

If the sum of odd numbered terms and the sum of even numbered terms in the expansion of  \[\left( x + a \right)^n\]  are A and B respectively, then the value of \[\left( x^2 - a^2 \right)^n\] is 

 

विकल्प

•  \[A^2 - B^2\]

• \[A^2 + B^2\]

•  4 AB

•  none of these

   

Answer 1

 \[A^2 - B^2\]

\[\text{ If A and B denote respectively the sums of odd terms and even terms in the expansion }  (x + a )^n \]

\[\text{ Then } , (x + a )^n = A + B . . . \left( 1 \right)\]

\[ (x - a )^n = A - B . . . \left( 2 \right)\]

\[\text{ Multplying both the equations we get} \]

\[ (x + a )^n (x - a )^n = A^2 - B^2 \]

\[ \Rightarrow ( x^2 - a^2 )^n = A^2 - B^2\]