Question

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

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

Short answer

Expansion is$81x^4-432x^3+288x^2-768x+256$

Step-by-step solution

Given Information

Expand binomial using Pascal's Triangle.

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

Solution

We have

Here the exponent is 4 hence we need to consider fifth row

The expansion is

$$\begin{gathered} (3x-4{)}^4=1{\left(3x\right)}^4+4{\left(3x\right)}^3\left(-4\right)+6{\left(3x\right)}^2{\left(-4\right)}^2+4·3x{\left(-4\right)}^3+1{\left(-4\right)}^4 \\ =81x^4-432x^3+288x^2-768x+256 \end{gathered}$$