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Question
If A and B are the sums of odd and even terms respectively in the expansion of (x + a)n, then (x + a)2n − (x − a)2n is equal to
Options
4 (A + B)
4 (A − B)
AB
4 AB
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Solution
4AB
\[\text{ If A and B denote respectively the sums of odd terms and even terms in the expansion } (x + a )^n \]
\[\text{ Then } , (x + a )^n = A + B . . . \left( 1 \right)\]
\[ (x - a )^n = A - B . . . \left( 2 \right)\]
\[\text{ Squaring and subtraction equation } \left( 2 \right) \text{ from} \left( 1 \right) \text{ we get } \]
\[ (x + a )^{2n} - (x - a )^{2n} = \left( A + B \right)^2 - \left( A - B \right)^2 \]
\[ \Rightarrow (x + a )^{2n} - (x - a )^{2n} = 4AB\]
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