Math Help - Difference of Squares

1. 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?

2. $a^2-b^2 \neq (a-b)^2$

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