Can you multiply this polynomial?

homerslippers
Mon, 06 Jul 2009 20:24:03 +0000

Expand to (t^3-1)(t^3+1)(t^3-1)(t^3+1)(t^3-1)(t^3+1)(t^3-1)(t^3+1)
Each of those is the factorization of a difference of two squares, so
(t^6-1)(t^6-1)(t^6-1)(t^6-1)
(t^6-1)^4

Use binomial theorem:
4C0(t^24) + 4C1(t^18)(-1) + 4C2(t^12)(-1)^2 + 4C1(t^6)(-1)^3 + 4C4(-1)^4
= t^24 - 4t^18 + 6t^12 - 4t^6 + 1

Gamma only made one mistake (fixed now–a wrong coeff)