Answer
(a.)$4x^2-36x+80$.
(b.)$4 x^3-36x^2+80x$.
Work Step by Step
The given values from the figure are
For the large rectangle.
Length $L=10-2x$.
Width $W=8-2x$.
Height $H=x$.
(a.) Formula for the area of the base is
$A=L\cdot W$
Plug all values.
$A=(10-2x)\cdot (8-2x)$
Simplify.
$A=10\cdot (8-2x)-2x\cdot (8-2x)$
$A=80-20x-16x+4x^2$
$A=4x^2-36x+80$.
(b.) Formula for the volume of the open box is
$V=L\cdot W\cdot H$
Plug all values.
$V=(10-2x)\cdot (8-2x)\cdot (x)$
Simplify
$V=(10-2x)\cdot (8\cdot x-2x\cdot x)$
$V=(10-2x)\cdot (8x-2 x^2)$
Clear the parentheses.
$V=10\cdot (8x-2 x^2)-2x\cdot (8x-2 x^2)$
$V=80x-20 x^2-16x^2+4 x^3$
Rearrange.
$V=4 x^3-36x^2+80x$.
