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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 (A) 4 (A + B) (B) 4 (A − B) (C) Ab (D) 4 Ab - Mathematics

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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

     
MCQ
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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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Chapter 18: Binomial Theorem - Exercise 18.4 [Page 46]

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RD Sharma Mathematics [English] Class 11
Chapter 18 Binomial Theorem
Exercise 18.4 | Q 5 | Page 46

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