Question

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

$(x+4{)}^4$

Short answer

Expansion is$x^4+16x^3+96x^2+256x+256$

Step-by-step solution

Given Information 

Expand binomial using Pascal's Triangle.

$(x+4{)}^4$

Solution

We have

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

The expansion is

$$\begin{gathered} (x+4{)}^4=1x^4+4x^3·4+6x^2·4^2+4x·4^3+1·4^4 \\ =x^4+16x^3+96x^2+256x+256 \end{gathered}$$