Question

The length of a rectangle field is represented by the expression 14 X minus 3X squared +2 Y. The width of the field is represented by the expression 5X minus 7X squared plus 7Y. How much greater is the length of the field than the width?

Answer 1

`9x+4x^2-5y`

Explanation:

Hi there!

Length of the field:
`14x-3x^2+2y` units

Width of the field:
`5x-7x^2+7y` units

To find how much greater the length of the field is than the width, subtract the width from the length:

`14x-3x^2+2y-(5x-7x^2+7y)`

Open up the parentheses

`= 14x-3x^2+2y-5x+7x^2-7y`

Combine like terms

`= 14x-5x-3x^2+7x^2+2y-7y\\= 9x+4x^2-5y`

Therefore, the length is
`9x+4x^2-5y` units greater than the width.

I hope this helps!