The total volume of the cubes in factored form is (4p + 2q^2)(16p^2 - 8pq^2 + 4q^4)
The volume of a figure or a three dimensional shape is the amount of space inside the figure or the three dimensional shape
The two cubes are stacked upon one another, so they form a composite figure.
The side lengths of the cubes are given as
Cube 1 = 4p
Cube 2 = 2q^2
The volume of each cube is calculated as:
Volume = Side length^3
So, the total volume is
Total = (4p)^3 + (2q^2)^3
Evaluate the exponents
Total = 64p^3 + 8q^6
Using the sum of cubes, we have the factored form to be
Total = (4p + 2q^2)(16p^2 - 8pq^2 + 4q^4)
Hence, the total volume of the cubes in factored form is (4p + 2q^2)(16p^2 - 8pq^2 + 4q^4)
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Complete 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?
