(y-2)^3 + 6(y-2)^2 + 12(y-2) + 8

Expanding the terms:

(y-2)^3 = (y-2)(y-2)(y-2)
= (y^2 - 4y + 4)(y-2)
= y^3 - 2y^2 - 4y^2 + 8y + 4y - 8
= y^3 - 6y^2 + 12y - 8

6(y-2)^2 = 6(y^2 - 4y + 4)
= 6y^2 - 24y + 24

12(y-2) = 12y - 24

Now, putting all the expanded terms together:

(y-2)^3 + 6(y-2)^2 + 12(y-2) + 8
= y^3 - 6y^2 + 12y - 8 + 6y^2 - 24y + 24 + 12y - 24 + 8
= y^3 + 12y