
Difference of Squares
Î need to simplify A^16  16 (That's A raised to the 16th power minus 16). I understand the difference of squares pattern. So I start by making it (A^8  4)^2 (That's A to the 8th power minus 4) squared. What I don't get is how if I simplified the "difference of squares" as it is now, I wouldn't get A^16  16. Does this make sense?

$\displaystyle a^2b^2 \neq (ab)^2$
Instead the difference of two square is $\displaystyle a^2b^2 = (ab)(a+b)$ so in your case it will be $\displaystyle (a^84)(a^8+4)$. Also note that the first term is also the difference of two squares