Question

A cube with side length 5h^2 is stacked on another cube with side length 3k What is the total volume of the cubes in factored form?

Answer 1

Answer:

(5h^2 + 3k)(25h^4 - 15h^2k + 9k^2)

Step-by-step explanation:

So, the formula for the volume(V) of a cube is V = a^3, where "a" is the length of one side. This is because, on a cube, each side/edge is the same length. (Just to clarify)

Now, the side of one cube is 5h^2. If you cube this value, you get (5h^2)^3. That is the volume of this cube.

Do the same with the other. 3k cubed = (3k)^3

Because this is an addition problem, you will be adding the values:

(5h^2)^3 + (3k)^3

To factor, you can use the sum of cubes formula:

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

*Make sure you pay attention to the negative sign!

After plugging it all in and simplifying, you should get

(5h^2 + 3k)(25h^4 - 15 h^2k + 9k^2)

Hope I helped!

Answer 2

Just find the volume of each cube separately and add together the results. First cube has side length 5h^2. What is the formula for the volume of a cube? Second cube has side length 3k. Whats its volume?