Answer
(a.) $x^2+7x+12$.
(b.) $x^2+3x+2$.
(c.) $4x+10$.
Work Step by Step
The given values from the figure are
For the large rectangle.
Length $L_1=x+4$
Width $W_1=x+3$
For the small unshaded rectangle.
Length $L_2=x+2$
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.
$A_1=(x+4)\cdot (x+3)$
Simplify.
$A_1=x\cdot (x+3)+4\cdot (x+3)$
$A_1=x^2+3x+4x+12$
$A_1=x^2+7x+12$.
(b.) Area of the small unshaded rectangle.
$A_2=L_2\cdot W_2$
Plug all values.
$A_2=(x+2)\cdot (x+1)$
Simplify.
$A_2=x\cdot (x+1)+2\cdot (x+1)$
$A_2=x^2+x+2x+2$
$A_2=x^2+3x+2$.
(c.) Area of the shaded blue region.
$=A_1-A_2$
$=x^2+7x+12-(x^2+3x+2)$
Clear the parentheses.
$=x^2+7x+12-x^2-3x-2$
Simplify.
$=4x+10$.
