Find the third term in the expansion of \((a - b)^{6}\) in ascending powers of b.
Question 1 Report
Find the third term in the expansion of \((a - b)^{6}\) in ascending powers of b.
Answer Details
To find the third term in the expansion of \((a-b)^6\) in ascending powers of b, we can use the binomial theorem, which states that:
\[(a-b)^6 = \sum_{n=0}^{6} {6 \choose n} a^{6-n}(-b)^n\]
The third term is the term where n=2, so we plug in n=2 into the above formula and simplify:
\[{6 \choose 2} a^{6-2}(-b)^2 = 15a^4b^2\]
Therefore, the third term in the expansion of \((a-b)^6\) in ascending powers of b is \(15a^4b^2\).
So the correct answer is option B, "15a^4b^2".
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