Question

Find the volume of a rectangular box whose length is a-2 inches, width is ‘ a ‘ inches and its height is a+3 inches.

Answer 1

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:
$(a - 2) \times (a) \times (a + 3)$
Work out the left two terms first:
(a-2)x(a) =
${a}^{2} - 2a$
Then multiply the height:
$({a}^{2} - 2a) \times (a + 3)$
$= {a}^{3} - 2 {a}^{2} + 3 {a}^{2} - 6a$
Collect like terms:
$= {a}^{3} + {a}^{2} - 6a$
Then factorise (if needed)
$= a( {a}^{2} + a - 6)$
$= a(a + 3)(a - 2)$
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:

${a}^{3} + {a}^{2} - 6a$
cubic inches
or a(a+3)(a-2) cubic inches

Hope this helped