Question

what is the coefficient of $x^3y^2$ in the expansion of $(x + y)^5$ using pascal’s triangle?
a. 5
b. 15
c. 20
d. 10

Explanation:

Step1: Recall Pascal's Triangle for \(n = 5\)

Pascal's Triangle rows correspond to \(n\) in \((x + y)^n\). The 5th row (starting from \(n = 0\)) is \(1, 5, 10, 10, 5, 1\).

Step2: Identify the term's position

In the expansion of \((x + y)^5\), the terms are \(x^5, x^4y, x^3y^2, x^2y^3, xy^4, y^5\). The coefficient of \(x^3y^2\) is the 3rd non - zero coefficient in the row (indexing from 0), which is 10.

Answer:

d. 10