Question

The figures below are rectangles. Which polynomial represents the area of the shaded region? HAVE ALL MY POINTS but answer truthfully cause i have the answer choices

Answer 1

`7x - 1`

Explanation:

Area of the shaded region = area of the large rectangular - area of the small rectangle

Area of rectangle is given as l*w

Area of the large rectangle =
`l*w = (x + 5)(x - 1)`

Expand

`= x(x - 1) +5(x - 1)`

`= x^2 - x + 5x - 5`

Area of large rectangle
`= x^2 + 4x - 5`

Area of small rectangle =
`l*w = (x + 1)(x - 4)`

`= x(x - 4) +1(x - 4)`

`= x^2 - 4x + x - 4`

Area of small rectangle =
`= x^2 - 3x - 4`

Area of shaded region =
`(x^2 + 4x - 5) - (x^2 - 3x - 4)`

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

Collect like terms

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

`= 7x - 1`