Chapter 8.3, Problem 44PPS

To determine

To complete: The table.

Answer to Problem 44PPS

  $\begin{array}{cc}\text{Expression}& {\left(\text{Expression}\right)}^2\\ x+5& x^2+10x+25\\ 3y+1& 9y^2+6y+1\\ z+q& z^2+2zq+q^2\end{array}$

Explanation of Solution

Given:

  $\begin{array}{cc}\text{Expression}& {\left(\text{Expression}\right)}^2\\ x+5& \\ 3y+1& \\ z+q& \end{array}$

Calculation:

Use the formula $\left(a+b\right)=a^2+2ab+b^2$ to find the square of each expression

The first expression is $\left(x+5\right)$

Use the above formula to find its square

  $\begin{array}{c}\left(x+5\right)=x^2+2x\cdot 5+5^2\\ =x^2+10x+25\end{array}$

Similarly the square of second expression is

  $\begin{array}{c}\left(3y+1\right)={\left(3y\right)}^2+2\cdot 3y\cdot 1+1^2\\ =9y^2+6y+1\end{array}$

And the square of the third expression is

  $\begin{array}{c}\left(z+q\right)=z^2+2\cdot z\cdot q+q^2\\ =z^2+2zq+q^2\end{array}$

So, the complete table is given by

  $\begin{array}{cc}\text{Expression}& {\left(\text{Expression}\right)}^2\\ x+5& x^2+10x+25\\ 3y+1& 9y^2+6y+1\\ z+q& z^2+2zq+q^2\end{array}$