Question

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

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

Short answer

Expansion is$27x^3-135x^2+225x-125$

Step-by-step solution

Given Information

Expand binomial using Pascal's Triangle.

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

Solution

We have

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

The expansion is

$$\begin{gathered} (3x-5{)}^3=1(3x{)}^3+3(3x{)}^2(-5)+3(3x\left)\right(-5{)}^2+1(-5{)}^3 \\ =27x^3-135x^2+225x-125 \end{gathered}$$