Factoring:
(a4 + 1) , Factor to the form a(b + c) foiling this you get (ab + ac) and ab = a4 and ac = 1
for ac =1 then both a and c = 1, solving for b, ab = a4 , (1)(b) = a4 , b = a4 factoring b out
you get ab ( b/b + c/b) but a and c =1, (1)(a4) [ (a4/a4 ) + (1/ a4)] =a4[ 1 + (1/a4)] to check this if you foil this you get [a4(1) + (a4)(1)/ a4] = a4 + 1
a4 - 64 can be written as (a2)2 - (8)2 this is of the form a12 - b12 = ( a1 + b1)( a1 - b1) where
a1 = a2 and b1 = 8 substitute you get ( a2+8)(a 2- 8) this is also difference of two squares to check if you foil this you get a2a2 - 8a2+8a2 -(8)(8) = a4 +0 - 64 = a4 - 64
