Answer
(a.) $x^2+12x+27$.
(b.) $x^2+6x+5$.
(c.) $6x+22$.
Work Step by Step
The given values from the figure are
For the large rectangle.
Length $L_1=x+9$
Width $W_1=x+3$
For the small unshaded rectangle.
Length $L_2=x+5$
Width $W_2=x+1$
Formula for the area of the rectangle is
$A=L\cdot W$
(a.) Area of the large rectangle.
$A_1=L_1\cdot W_1$
Plug all values.
$A_1=(x+9)\cdot (x+3)$
Simplify.
$A_1=x\cdot (x+3)+9\cdot (x+3)$
$A_1=x^2+3x+9x+27$
$A_1=x^2+12x+27$.
(b.) Area of the small unshaded rectangle.
$A_2=L_2\cdot W_2$
Plug all values.
$A_2=(x+5)\cdot (x+1)$
Simplify.
$A_2=x\cdot (x+1)+5\cdot (x+1)$
$A_2=x^2+x+5x+5$
$A_2=x^2+6x+5$.
(c.) Area of the shaded blue region.
$=A_1-A_2$
$=x^2+12x+27-(x^2+6x+5)$
Clear the parentheses.
$=x^2+12x+27-x^2-6x-5$
Simplify.
$=6x+22$.
