Question

A school's rectangular athletic field has a length of 125 yards and a width of 75 yards. The planning committee has decided to expand both the length and the width of the field by a certain number of yards ... say x. Write a polynomial in standard form representing the area of the new field.

Answer 1

x^2 + 200x + 9375 = y

Explanation:

So, if the original area is 125*75, and you are changing this by adding x to both sides, we can create a new equation to model this change. the length changes to (125+x) and the width to (75+x). This gives us the expression (x+125)(x+75) = y, or x^2 + 200x + 9375 = y, where y is the total area of the field.

Answer 2

Explanation:

A school's rectangular athletic field has a length of 125 yards and a width of 75 yards. The planning committee has decided to expand both the length and the width of the field by a certain number of yards ... say x. This means that the new length would be 125 + 2x and the new width would be 75 + 2x

Therefore, the new area would be

A(x) = (125 + 2x)(75 + 2x) = 9375 + 250x + 150x + 4x^2

A(x) = 4x^2 + 400x + 9375