Question

use pascals triangle to complete the expansion of $(t + u)^2$.
$t^2 + \square tu + u^2$

Explanation:

Step1: Recall Pascal's Triangle for power 2

Pascal's Triangle rows correspond to binomial powers. For \((a + b)^n\), the coefficients are from the \(n\)-th row (starting from row 0). For \(n = 2\), the row is \(1, 2, 1\).

Step2: Apply to \((t + u)^2\)

The expansion of \((t + u)^2\) using the coefficients \(1, 2, 1\) is \(1 \cdot t^2 + 2 \cdot tu + 1 \cdot u^2\). So the coefficient of \(tu\) is \(2\).

Answer:

\(2\)