Question

question 10 of 10
the coefficients in the expansion of ((x + y)^6) are ____.

a. 0, 6, 15, 20, 15, 6, 0
b. 0, 1, 6, 15, 15, 6, 1, 0
c. 1, 6, 15, 20, 15, 6, 1
d. 1, 6, 15, 15, 6, 1

Explanation:

Step1: Recall binomial theorem

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

Step2: Calculate coefficients for $n=6$

$\binom{6}{0}=1$, $\binom{6}{1}=6$, $\binom{6}{2}=15$, $\binom{6}{3}=20$, $\binom{6}{4}=15$, $\binom{6}{5}=6$, $\binom{6}{6}=1$.

Step3: Match with options

The coefficients are 1,6,15,20,15,6,1.

Answer:

C. 1,6,15,20,15,6,1