The volume of a rectangular prism, in this case the box, is just length x width x height.
We know all three:
L = a-2
W = a
H = a+3
Therefore the volume is:
[tex](a - 2) \times (a) \times (a + 3)[/tex]
Work out the left two terms first:
(a-2)x(a) =
[tex] {a}^{2} - 2a[/tex]
Then multiply the height:
[tex] ({a}^{2} - 2a) \times (a + 3) [/tex]
[tex] = {a}^{3} - 2 {a}^{2} + 3 {a}^{2} - 6a[/tex]
Collect like terms:
[tex] = {a}^{3} + {a}^{2} - 6a[/tex]
Then factorise (if needed)
[tex] = a( {a}^{2} + a - 6)[/tex]
[tex] = a(a + 3)(a - 2)[/tex]
See how the final answer is the same as the length, witdh and height? That's a good way to check your work.
So the volume is:
[tex] {a}^{3} + {a}^{2} - 6a[/tex]
cubic inches
or a(a+3)(a-2) cubic inches
Hope this helped
