Question

In the following exercises, expand each binomial.

$(x+y{)}^3$

Short answer

Expansion is$x^3+3x^{2}y+3x{y}^2+y^3$

Step-by-step solution

Step 1. Given Information

Expand$(x+y{)}^3$

Step 2. Solution 

We have

$$\begin{gathered} (x+y{)}^3=\left(\begin{array}{l}3\\ 0\end{array}\right)x^{3-0}{y}^{3-3}+\left(\begin{array}{l}3\\ 1\end{array}\right)x^{3-1}{y}^{3-2}+\left(\begin{array}{l}3\\ 2\end{array}\right)x^{3-2}{y}^{3-1}+\left(\begin{array}{l}3\\ 3\end{array}\right)x^{3-3}{y}^{3-0} \\ =x^3+3x^{2}y+3x{y}^2+y^3 \end{gathered}$$