Answer
$4x+10$
Work Step by Step
The shaded area is the area of the bigger rectangle minus the area of the smaller rectangle.
Thus, the area $A_1$ of the bigger rectangle is:
$(x+4)(x+3)=x^2+3x+4x+12$
$=x^2+7x+12.$
The area $A_2$ of the smaller rectangle is:
$A_2=(x+2)(x+1)$
$=x^2+x+2x+2$
$=x^2+3x+2.$
Now we can calculate the shaded area:
$A_1-A_2=(x^2+7x+12)-(x^2+3x+2)$
$=x^2+7x+12-x^2-3x-2$
$=4x+10.$
