Question

question 18 of 25
the coefficients corresponding to k = 0, 1, 2, ..., 5 in the expansion of (x + y)^5 are ______.

a. 0, 1, 5, 10, 5, 1, 0

b. 0, 5, 10, 10, 5, 0

c. 1, 5, 10, 10, 5, 1

d. 1, 5, 10, 5, 1

Explanation:

Step1: Recall binomial theorem

The expansion of $(x+y)^n$ uses binomial coefficients $\binom{n}{k}$ for $k=0,1,...,n$.

Step2: Calculate coefficients for $n=5$

Compute $\binom{5}{0}=1$, $\binom{5}{1}=5$, $\binom{5}{2}=10$, $\binom{5}{3}=10$, $\binom{5}{4}=5$, $\binom{5}{5}=1$.

Step3: Match with options

The coefficients are 1,5,10,10,5,1.

Answer:

C. 1,5,10,10,5,1