Question

He perimeter of a rectangle is represented by 4x2 + 5x ? 2. The perimeter of a smaller rectangle is represented by x2 + 3x + 5. Which polynomial expression BEST represents how much larger the first rectangle is than the smaller rectangle?

Answer 1

The perimeter of first rectangle is
`3x^2+2x-7` much larger than the smaller rectangle.

Explanation:

The perimeter of a rectangle is represented by

`4x^2+5x-2`

The perimeter of a smaller rectangle is represented by

`x^2+3x+5`

The difference of perimeter of rectangle and smaller rectangle is

`4x^2+5x-2-(x^2+3x+5)`

`4x^2+5x-2-x^2-3x-5`

Combine like terms.

`(4x^2-x^2)+(5x-3x)+(-2-5)`

`3x^2+2x-7`

The perimeter of first rectangle is
`3x^2+2x-7` much larger than the smaller rectangle.