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

Answer:

$(x^{2}-x-2)\ units^{2}$

Step-by-step 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

$A1-A2=(2x^{2}+5x+3)-(x^{2}+6x+5)=(x^{2}-x-2)\ units^{2}$