The difference of cubes states that a^3-b^3 = (a-b)(a^2+ab+b^2)

So I have the problem to factor, which is:

y^6-13y^3+40

I factored and got this:

(y^3-8)(y^3-5)

That first term is the difference of cubes so the formula should work, but I used it and got:

(y-2)(y^2+2y+4)(y^3-5) BUT.....

my answer key says it should be (y-2)(y^4+2y+4)(y^3-5)

I don't understand why it's y^4 here. It's probably simple, I know, but I've been doing this stuff all day and I think my brain is fried. I'm in my 30's trying to reteach myself this stuff after a long time of ignoring it. Any help would be appreciated. Thanks.