Answer
$6x+22$
Work Step by Step
The area of the shaded region is the area of the bigger rectangle minus the area of the smaller rectangle.
Thus, the area $A_1$ of the bigger rectangle is:
$(x+9)(x+3)=x^2+3x+9x+27$
$=x^2+12x+27.$
The area $A_2$ of the smaller rectangle is:
$A_2=(x+5)(x+1)$
$=x^2+x+5x+5$
$=x^2+6x+5.$
Now we can calculate the shaded area:
$A_1-A_2=(x^2+12x+27)-(x^2+6x+5)$
$=x^2+12x+27-x^2-6x-5$
$=6x+22.$
