a^3-a^2-4a+4 = a^2(a-1)-4(a-1) = (a-1)(a^2-4) = (a-1)(a-2)(a+2)b^4-b^2-2b-1 = b^2(b^2-1)-1(b^2-1) = (b^2-1)(b^2-1) = (b-1)(b+1)(b-1)(b+1) = (b-1)^2(b+1)^24b^2-2b-1 = 4b^2-4b+2b-1 = 4b(b-1)+1(2b-1) = (4b+1)(b-1)
a^3-a^2-4a+4 = a^2(a-1)-4(a-1) = (a-1)(a^2-4) = (a-1)(a-2)(a+2)
b^4-b^2-2b-1 = b^2(b^2-1)-1(b^2-1) = (b^2-1)(b^2-1) = (b-1)(b+1)(b-1)(b+1) = (b-1)^2(b+1)^2
4b^2-2b-1 = 4b^2-4b+2b-1 = 4b(b-1)+1(2b-1) = (4b+1)(b-1)