Question

A glass container can hold 216a^3 cubic cm of water. inside the glass container is a metallic cube with a volume of 64b^3 cubic cm. How much water you will be able to fill the glass container with the metallic cube inside? Express your answer in factored form.​

Answer 1

`16(3a-2b)(4a^2+3ab+2b)`

Explanation:

We will be able to fill the glass up to the amount of water possible to hold in the glass, minus the amount in the cube. This means it will be able to hold
`216a^3-64b^3=(6a)^3-(4b)^3`cubic cm of water.

Using the difference of cubes formula(you can prove this by expanding back out again), we get that
`(6a^3)-(4b)^3=(6a-4b)((6a)^2+(6a)(4b)+(4b)^2)=(6a-4b)(36a^2+24ab+16b)=8(6a-4b)(4a^2+3ab+2b)=16(3a-2b)(4a^2+3ab+2b)`

Therefore, the answer is
`\boxed{16(3a-2b)(4a^2+3ab+2b)}` cubic centimeters and we're done!