Question

The area of the shaded portion of the rectangle is how many units larger than the area of the unshaded portion of the rectangle?

Answer 1

`(x^(2)-x-2)\ units^(2)`

Explanation:

step 1

Calculate the area of the shaded portion

`A1=(2x+3)(x+1)\\ \\A1=2x^(2)+2x+3x+3\\ \\A1=(2x^(2)+5x+3)\ units^(2)`

step 2

Calculate the area of the unshaded portion

`A2=(x+5)(x+1)\\ \\A2=x^(2)+x+5x+5\\ \\A2=(x^(2)+6x+5)\ units^(2)`

step 3

Find the difference of the areas

`A1-A2=(2x^(2)+5x+3)-(x^(2)+6x+5)=(x^(2)-x-2)\ units^(2)`