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:
