Question

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

$(x-y{)}^5$

Short answer

The expansion is$x^5-5x^{4}y+10x^3{y}^2-10x^2{y}^3+5x{y}^4-y^5$

Step-by-step solution

Given Information

Expand binomial using Pascal's Triangle.

$(x-y{)}^5$

Solution

We have

The exponent is 5 hence sixth row need to be considered

The expansion is

$$\begin{gathered} (x-y{)}^5=1x^5+5x^4\left(-y\right)+10x^3{\left(-y\right)}^2+10x^2{\left(-y\right)}^3+5x{\left(-y\right)}^4+1{\left(-y\right)}^5 \\ =x^5-5x^{4}y+10x^3{y}^2-10x^2{y}^3+5x{y}^4-y^5 \end{gathered}$$