Chapter 8.3, Problem 35PPE

To determine

To find: The polynomial in standard form that represents the area of the expanded athletic field.

Answer to Problem 35PPE

  $x^2+200x+9375$

Explanation of Solution

Given information: A school’s rectangular athletic fields currently have a length of 125 yd and a width of 75 yd. The school plans to expand both the length and width of the field by x yards.

Calculation:

The expanded length of the field is $(125+x)$ yards.

The expanded width of the field is $(75+x)$ yards.

Then, the area of the expanded field is,

  $\begin{array}{l}(125+x)(75+x)\\ =125\cdot 75+125\cdot x+x\cdot 75+x\cdot x[\text{by FOIL method]}\\ =9375+125x+75x+x^2\\ =9375+200x+x^2[\text{combining like terms]}\\ =x^2+200x+9375\end{array}$

Thus, the area of the expanded athletic field is $x^2+200x+9375$ .