The coefficients corresponding to k = 0, 1, 2, 5 in the expansion of (x + y)^5 are
a. 1, 5, 10, 10, 5, 1
b. 1, 5, 10, 5, 1
c. 0, 1, 5, 10, 5, 1, 0
d. 0, 5, 10, 10, 5, 0

The coefficients corresponding to k = 0, 1, 2, ..., 5 in the expansion of (x + y)^5 are 1, 5 , 10 , 10, 5, 1. The coefficients can be solve using manual expansion of the term of using combination:

A. 1, 5, 10, 10, 5, 1

Step-by-step explanation:

By the binomial expansion,

Where,

Here, n = 5 and k = 0,1,2,......, 5.

Thus,

    ( Because, )

Thus, the coefficients are 1, 5, 10, 5, 1.

⇒ Option A is correct.

square pyramid

step-by-step explanation:

square prism looks like nothing like that

triangular prism has a rectangular base instead of a square base

tetrahedron has a triangular base