Question

Factor the expression

Answer 1

Explanation:

Your difference of perfect cubes formula is given as

`(a-b)(a^2+ab+b^2)` and you have already correctly identified a as
`5q^2` and b as
`r^2s`. So we fill in the formula as follows:

`(5q^2-r^2s)((5q^2)^2+(5q^2)(r^2s)+(r^2s)^2)` and we simplify. Remember that

`(5q^2)^2=(5)^2*(q^2)^2=25q^4`. It's important that you remember the rules.

Simplifying then gives us

`(5q^2-r^2s)(25q^4+5q^2r^2s+r^4s^2)`

That's it, so fill it in however you need to on your end. Learn the patterns for the sum and difference of cubes and it will save you a ton of headaches...promise!!