Part a
we have that
the volume of the box is equal to
V=L*W*H
so
In this problem
the height H is equal to H=x
L=(10-2x) in
W=(8-2x) in
substitute in the formula
V=(10-2x)(8-2x)(x) in3
apply distributive property
V=(80-20x-16x+4x^2)(x)
V=(4x^3-36x^2+80x) in3
Part b
For x=0.7 in
V=4(0.7)^3-36(0.7)^2+80(0.7)
V=39.732 in3
For x=2.3 in
V=4(2.3)^3-36(2.3)^2+80(2.3)
V=42.228 in3
so
the change in the box volume increases (42.228-39.732)=2.5 in3
For x=3.2 in
V=4(3.2)^3-36(3.2)^2+80(3.2)
V=18.432 in3
the change in the box volume decreases (42.228-18.432)=23.8 in3