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

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

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calculista

Answer:

[tex](x^{2}-x-2)\ units^{2}[/tex]

Step-by-step explanation:

step 1

Calculate the area of the shaded portion

[tex]A1=(2x+3)(x+1)\\ \\A1=2x^{2}+2x+3x+3\\ \\A1=(2x^{2}+5x+3)\ units^{2}[/tex]

step 2

Calculate the area of the unshaded portion

[tex]A2=(x+5)(x+1)\\ \\A2=x^{2}+x+5x+5\\ \\A2=(x^{2}+6x+5)\ units^{2}[/tex]

step 3

Find the difference of the areas

[tex]A1-A2=(2x^{2}+5x+3)-(x^{2}+6x+5)=(x^{2}-x-2)\ units^{2}[/tex]