Need major help factoring (Algebra 2)?

Question

Can somebody help me factor both of these and explain how to?
All exponents with over 1 character in brackets.

h^2r^8-k^(2/3)r^8-h^2s+k^(2/3)s
4x^2+9y^2

Answer 1

Look for common terms and factor them out. For this one, you'll have to factor out in parts - factor the first two by themselves, and the last two by themselves, and then see what you have from there:

h^2r^8 - k^(2/3)r^8 - h^2s + k^(2/3)s = [h^2r^8 - k^(2/3)r^8] - [h^2s - k^(2/3)s]
= r^8(h^2 - k^(2/3)) - s(h^2 - k^(2/3))
= (r^8 - s)(h^2 - k^(2/3))

The second one can't be factored. There is a rule for the difference of squares, but not for the sum of squares. If that + was a -, then it'd factor out as (2x - 3y)(2x + 3y). But since it's a +, you can't factor that ant further than it is.