Question

The coefficients in the expansion of (x + y)⁵ are__

A. 1, 5, 10, 10, 5, 1
B. 1, 5, 10, 5, 1
C. 0, 5, 10, 10, 5, 0
D. 0, 1, 5, 10, 5, 1, 0

Answer 1

The coefficients in the expansion of (x + y)⁵ are determined by the binomial theorem and correspond to the entries in the 5th row of Pascal's Triangle, which are A. 1, 5, 10, 10, 5, 1.

Step-by-step explanation:

The coefficients in the expansion of (x + y)⁵ can be determined by using the binomial theorem. According to the binomial theorem, when a binomial is raised to a power n, the coefficients for the expanded terms can be found as the entries in the nth row of Pascal's Triangle or by computing combinations. For the fifth power, the coefficients correspond to the combinations of 5 taken 0, 1, 2, 3, 4, and 5 at a time respectively, which are 1, 5, 10, 10, 5, and 1. Therefore, the correct answer is A. 1, 5, 10, 10, 5, 1.