So I think you’d just multiply out everything in there and then start collecting like terms. I’m not sure but I think you may have made an error in the first one (is that supposed to be 2x^2y, or 2x + 2y) so I’ll do the second one and the last one, and you can do the rest.

6ab(a^2 + b^2) = 6a^3b + 6ab^3.

(2ab + c)(2ab – c) = 4(a^2)(b^2) + 2abc – 2abc – c^2 = 4(a^2)(b^2) – c^2.

If that’s what you mean by simplify then I think that’s it.

As for a tutorial… I did a google search on “simplifying polynomials” and found this:

http://www.curriculum.org/tcf/teachers/projects/algebra/polynomialflash.adp

Check it out 🙂

Edit: To the person below me… “Maverick”, I’m not incorrect on the last one. How can I be? Your answer and mine are exactly the same. Please read again, thanks.

#1 are you telling me that the problem is -2y(-2x to power of 2y+3????

#2 person above was correct. You need only to multiply the 6ab by each of the entities within the parenthesis.

#3 you first need to multiply each of the entitites in the left paren, by each of the entities within the right paren and then combine like terms.

(a^3)b + a(b^3) +3ab – (a^2)b -b^3 -3b

since there are no like terms, there is nothing to combine and this is the final answer

#4 This is the classic FOIL (first, outer, inner, last) multiplication.

First = 4(a^2)(b^2)

Outer = -2abc

Inner = +2abc

Last = -c^2

since the inner and outer cancel each other out (added together they equal zero), the answer is

4(a^2)(b^2) – c^2

Note: I had to put the parenthesis around the a^2 to eliminate the confusion as in number 1

Good luck