Question

In the following exercises, expand each binomial using Pascal's Triangle.

$(4x-1{)}^3$

Short answer

Expansion is$64x^3-48x^2+12x-1$

Step-by-step solution

Given Information

Expand binomial using Pascal's Triangle.

$(4x-1{)}^3$

Solution

We have

Here the exponent is 3 hence we need to consider fourth row

The expansion is

$$\begin{gathered} (4x-1{)}^3=1{\left(4x\right)}^3+{3\left(4x\right)}^2(-1)+3\left(4x\right){(-1)}^2+(-1) \\ =64x^3-48x^2+12x-1 \end{gathered}$$