Answer:
\((4p+2q^2)(16p^2-8pq^2+4q^4)\)
Step-by-step 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 \((4p+2q^2)(16p^2-8pq^2+4q^4)\).
