Question

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

$(3x-1{)}^5$

Short answer

Expansion is$243x^5-405x^4+270x^3-90x^2+15x-1$

Step-by-step solution

Given Information

Expand binomial using Pascal's Triangle.

$(3x-1{)}^5$

Solution

We have

Here the exponent is 5 hence we need to consider sixth row

The expansion is

$$\begin{gathered} (3x-1{)}^5=1(3x{)}^5+5{\left(3x\right)}^4(-1)+10{\left(3x\right)}^3{(-1)}^2+{10\left(3x\right)}^2{(-1)}^3+5\left(3x\right){(-1)}^4+{1(-1)}^5 \\ =243x^5-405x^4+270x^3-90x^2+15x-1 \end{gathered}$$