Again, this question if from my final practice exam.
Factor Completely. $$81x^4-256y^4$$
I'm able to get this far, How do I know which of the two factors should be factored further. $$(9x^2+16y^2)(9x^2-16y^2)$$
Answer Key: $$(3x-2y)(3x+2y)(9x^2+4y^2)$$
A difference of squares is always factorable into two binomial factors. This immediately tells you that $9x^2 - 16y^2$ can be factored further.
A sum of squares cannot be factored into two binomials, and in your case $9x^2 + 16y^2$ has no common factor to pull out, nor can it be factored in any other way.
As Lubin points out below, there are sums of squares that are factorable, however, so a sum of squares should not be immediately discounted as not factorable.