Algebra
# Algebraic Manipulation

If $a+b+c=1, a^2+b^2+c^2=11,$ and $abc=2,$ what is the value of $a^2b^2+b^2c^2+c^2a^2?$

If $x^8 = 829$, what is $(x-1)(x+1)(x^2+1)(x^4+1)$?