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BINOMIAL THEOREM — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBINOMIAL THEOREM1 Mark
MCQ
If A and B are the sums of odd and even terms respectively in the expansion of $(\text{x}+\text{a})^{\text{n}},$ then $(\text{x}+\text{a})^{\text{2n}}-(\text{x}-\text{a})^{2\text{n}}$ is equal to:
  • A
    4(A + B)
  • B
    4(A - B)
  • C
    AB
  • ✓
    4AB
✓

Answer

Correct option: D.
4AB
If A and B denote respectively the sums of odd terms and even terms in the expansion $(\text{x}+\text{a})^{\text{n}}$
Then, $(\text{x}+\text{a})^{\text{n}}=\text{A}+\text{B}\ ...(\text{i})$
$(\text{x}-\text{a})^{\text{n}}=\text{A}-\text{B}\ ...(\text{ii})$
Squaring and subtraction equation (ii) from(i) we get,
$ (\text{x}+\text{a})^{2\text{n}}-(\text{x}-\text{a})^{2\text{n}}=(\text{A}+\text{B})^{2}-(\text{A}-\text{B})^{2}$
$\Rightarrow (\text{x}+\text{a})^{2\text{n}}-(\text{x}-\text{a})^{2\text{n}}=4\text{AB}$

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