Question

A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?

Answer 1

This question obviously requires fewer than forty words to answer fully, but to fulfil the criteria above I will explain it a bit further. The total volume is the side length to the third power of the first cube, plus the side length to the third power of the second cube: 4p^3+(2q^2)^3

Answer 2

`(4p+2q^2)(16p^2-8pq^2+4q^4)`

Explanation:

We have been given that a cube with side length 4p is stacked on another cube with side length
`2q^2`. We are asked to find the total volume of cubes in factored form.

We know that volume of cube is
`a^3`, where a represents length of each side of cube.

The sum of cubes would be:
`(4p)^3+(2q^2)^3`

Now, we will use sum of cubes formula to factor the volume of both cubes.

`a^3+b^3=(a+b)(a^2-ab+b^2)`

We can see that in the expression for volume of cubes
`a=4p` and
`b=2q^2`.

`(4p)^3+(2q^2)^3=(4p+2q^2)((4p)^2-(4p*2q^2)+(2q^2)^2)`

Simplifying our given expression, we will get:

`(4p)^3+(2q^2)^3=(4p+2q^2)(16p^2-8pq^2+4q^4)`

Therefore, the total volume of the cubes would be
`(4p+2q^2)(16p^2-8pq^2+4q^4)`.