Question:
If the sum of odd numbered terms and even numbered terms in the expansion of (x+a)ⁿ are A and B respectively, then the value of (x²-a²)ⁿ is
If the sum of odd numbered terms and even numbered terms in the expansion of (x+a)ⁿ are A and B respectively, then the value of (x²-a²)ⁿ is
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Use sum–difference identities for odd/even binomial terms.
Updated On: Mar 20, 2026
- \(A^2-B^2\)
- \(A^2+B^2\)
- \(4AB\)
- None
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The Correct Option is A
Solution and Explanation
Step 1: A=((x+a)ⁿ+(x-a)ⁿ)/(2), B=((x+a)ⁿ-(x-a)ⁿ)/(2)
Step 2: (x²-a²)ⁿ=(x+a)ⁿ(x-a)ⁿ=A²-B²
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