\begin{tabular}{|l} I can expand binomials using Pascal's Triangle. \\ Expand \( (4 x-5)^{3} \) using Pascal's Triangle. \\ \hline\end{tabular}

To expand \( (4x - 5)^3 \) using Pascal's Triangle, we first look at the third row of Pascal’s Triangle, which is \( 1, 3, 3, 1 \). This tells us the coefficients for our expansion. So, we’ll apply the binomial theorem: \[ (4x - 5)^3 = \sum_{k=0}^{3} \binom{3}{k} (4x)^{3-k} (-5)^{k} \] Calculating each term with the coefficients: 1. For \( k=0 \): \( 1 \cdot (4x)^3 \cdot (-5)^0 = 64x^3 \) 2. For \( k=1 \): \( 3 \cdot (4x)^2 \cdot (-5)^1 = -240x^2 \) 3. For \( k=2 \): \( 3 \cdot (4x)^1 \cdot (-5)^2 = 300x \) 4. For \( k=3 \): \( 1 \cdot (4x)^0 \cdot (-5)^3 = -125 \) Putting it all together gives us: \[ (4x - 5)^3 = 64x^3 - 240x^2 + 300x - 125 \]