Question

Factor the expression

Answer 1

Answer:

Step-by-step 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!!