Chapter 4.3, Problem 65PPS

To determine

To calculate: The expression for the area of the figure that remains when a square is cut off from the square in the figure and factor of the expression so formed.

  

Answer to Problem 65PPS

The expression for the remaining area is $x^2-36$ and factor of the expression is $\left(x+6\right)\left(x-6\right)$ .

Explanation of Solution

Given information:

A square is cut off from the figure,

  

Formula used:

Area of a square with side s is given by $\text{A}=s^2$ .

Factorization formula for difference of squares $A^2-B^2=\left(A+B\right)\left(A-B\right)$ .

Calculation:

Consider the given information that a square is cut off from the figure,

  

Recall that area of a square with side s is given by $\text{A}=s^2$ .

Area of the square with side x is ,

  $\text{A}=x^2$

And the area of the square with side 6 units that is cut off is,

  $\begin{array}{c}\text{A}=6^2\\ =36\end{array}$

Area of the remaining figure is calculated as,

  $x^2-36$

Therefore, expression for the remaining area is $x^2-36$ .

Recall factorization formula for difference of squares $A^2-B^2=\left(A+B\right)\left(A-B\right)$ .

Apply it,

  $x^2-36=\left(x+6\right)\left(x-6\right)$

Thus, the expression for the remaining area is $x^2-36$ and factor of the expression is $\left(x+6\right)\left(x-6\right)$ .