Chapter 9.2, Problem 1QR

Solution

To identify: Expand form of the binomial ${\left(x+y\right)}^2$ by using the distributive property.

The Expanded form of the binomial is $x^2+2xy+y^2$ .

Given information:

The given binomial is ${\left(x+y\right)}^2$ .

Explanation:

Rewrite as ${\left(x+y\right)}^2=\left(x+y\right)\left(x+y\right)$

By the distributive property $a\left(b+c\right)=ab+ac$

So expand as ${\left(x+y\right)}^2$

  $\begin{array}{l}{\left(x+y\right)}^2=x\left(x+y\right)+y\left(x+y\right)\\ {\left(x+y\right)}^{2}x\left(x\right)+y\left(x\right)+x\left(y\right)+y\left(y\right)\\ {\left(x+y\right)}^2=x^2+xy+xy+y^2\\ {\left(x+y\right)}^2=x^2+2xy+y^2\end{array}$

Expanded the binomial is $x^2+2xy+y^2$