Question

What is the coefficient of the third term in the binomial expansion of (a + b)⁶? group of answer choices

O 1
O 20
O 90
O 15

Answer 1

The coefficient of the third term in the binomial expansion of (a + b)⁶ is 15. This is calculated using the binomial theorem formula to find the binomial coefficient for the given term. The correct answer is option O 15

Step-by-step explanation:

The question concerns the coefficient of the third term in the binomial expansion of the expression (a + b)⁶.

In the binomial theorem, the nth term of the expansion of (a + b) raised to the power of m is given by the formula:
mCk ⋅ a⁽(⁰+k) ⋅ b⁹, where mCk represents the binomial coefficient and is calculated as m! / (k!(m-k)!).

The third term corresponds to k=2 (since we start counting from k=0 for the first term). By applying the formula, we find the binomial coefficient for the third term: 6C2 = 6! / (2!(6-2)!) = 6 ⋅ 5 / (2 ⋅ 1) = 15.

Therefore, the coefficient of the third term is 15, making it the correct answer to this binomial expansion problem.