Answer
(a.) $4x^2-26x+40$.
(b.) $4 x^3-26x^2+40x$.
Work Step by Step
The given values from the figure are
For the large rectangle.
Length $L=8-2x$.
Width $W=5-2x$.
Height $H=x$.
(a.) Formula for the area of the base is
$A=L\cdot W$
Plug all values.
$A=(8-2x)\cdot (5-2x)$
Simplify.
$A=8\cdot (5-2x)-2x\cdot (5-2x)$
$A=40-16x-10x+4x^2$
$A=4x^2-26x+40$.
(b.) Formula for the volume of the open box is
$V=L\cdot W\cdot H$
Plug all values.
$V=(8-2x)\cdot (5-2x)\cdot (x)$
Simplify
$V=(8-2x)\cdot (5\cdot x-2x\cdot x)$
$V=(8-2x)\cdot (5x-2 x^2)$
Clear the parentheses.
$V=8\cdot (5x-2 x^2)-2x\cdot (5x-2 x^2)$
$V=40x-16 x^2-10x^2+4 x^3$
Rearrange.
$V=4 x^3-26x^2+40x$.