Question

use pascals triangle to complete the expansion of $(y + z)^4$.
$y^4 + 4y^3z + \square y^2z^2 + 4yz^3 + z^4$

Explanation:

Step1: Recall Pascal's Triangle for power 4

Pascal's Triangle rows correspond to binomial coefficients. For \((a + b)^n\), the coefficients are from the \(n\)-th row (starting from row 0). For \(n = 4\), the row of Pascal's Triangle is \(1, 4, 6, 4, 1\).

Step2: Identify the coefficient for \(y^2z^2\)

In the expansion of \((y + z)^4\), the term \(y^2z^2\) has a coefficient equal to the third element (index 2, 0 - based) of the row for \(n = 4\), which is 6.

Answer:

6