Rosenbloomster

I believe that I have these factored out correctly, but I would appreciate someone checking my work:

First:

6ax^4 + 3ax^3y + 3ax^2y^2 = (3ax^2)(2x^2+3xy+y^2)

Second:

27x^3 - y^3 = (3x-y)^3

Third: x^2 -6xy +9y^2 -4 = x(x-6y) + (3y-2)^2 (something about this one seems wrong to me.)

I really appreciate any insight; I'm not in a class, but trying to recall this from years and years ago...

Thanks in advance!

I'm reviewing Algebra (definitely "use it or lose it" type skill.. and it's been years since I took college math) I'm trying to re-teach it to myself using my old math books from college and a couple of "dummies" algebra, but I'd appreciate anyone who is willing to write out steps that I'm not understanding. I do a lot of stochiometry, (I'm a chemistry graduate student!!!!!), but some of the rarely-used in my real life basic algebra is making me insane :)

Anyhow, this week I'm re-learning factoring, and I'm not in any classes; I'm working on this on my own. I can do it 90% of the time with no problem, but I get hung up occasionally.

So, my questions are:

1. Can 2c^3 + 5c^2 - 2c - 5 be factored at all? I'm not finding anything, but it seems to me that I should be finding something.

2.. For the expression 18x^2 + 3x - 10, I can't find a common factor, but I just *know* it's there staring me in the face.

Any input would be appreciated!

Thanks in advance!

This may be hard to type out so here goes:

(1/z + 1)^ 2 - 2(1/z + 1) = 3

Which I solved to get this equation:

(1/2 z^2) - 2z - 4

then I put it into quadratic equation and came up with the answer of 2 plus or minus the square root of 12.

I think it's right, but would someone double check for me?

I don't want to have someone do my work for me, but would someone mind checking my problem? I solved using the quadratic equation, but I haven't solved any problems using the quadratic equation, or algebra at all, in probably 15 years.

solve for x: 3x^2^ = 4x + 4

I got (4 plus/minus 2 times the square root of 3)/ over 6.

Am I within a million miles of the answer?

Thanks in advance?

I have a college algebrea review book, but this isn't making sense to me. I'm getting ready to take placement tests and trying to brush up on this stuff, as I'm stunned at how little I remember.

I appreciate anyone's help. I'd appreciate it if you have the time to explain the steps.

Thanks so much!