I have a rocks for jocks algebra math book. The one issue I have with this book is that in the practice plus area there are always problems that I have never seen and haven't been given any chapter in which to reference to get the right answer. An example of this is the following problem: (x-7)^2-4a^2.
What I do to solve this problem, I think, is to square everything in (x-7)(x+7) then add the -4a^2. After that I end up with -4a^2+x^2-49. Now I'm thinking this is the wrong answer, which it is, and I know I need to reduce it further. The problem is that I don't know how to do that; I know how to factor when it comes to things that will factor usually easily but this I do not have any idea. The answer is (x-7-2a)(x-7+2a). I have looked through multiplying polynomials and all it shows is how to multiply polynomials that look like that. I haven't once seen a problem in any of the chapter examples before to help me with this. I would like to learn this stuff, but it seems like a huge joke that the writers of the book play just to get their daily fix.
Another problem is y^7+y. I look for a common factor "y" and I factor it out so then I'm left with y(y^6+1). This is where I am stuck. I don't know the process that will allow me to arrive at the answer of y(y^2+1)(y^4-y^2+1). I have the instructor book which is why I know the answer, but I don't understand how they get the answer because I cannot find it in the book. Why couldn't it have been reduced to (y^3+1) or (y^4+1)? These are the questions I have and I can not ever find an answer for them in the book. I understand factoring down to lowest terms is ideal, but what do I do after I factor to (y^2+1). Where does the rest of it go? Seems like it is a huge secret. I try to ask people who are good at math in chat-rooms but all they say are it just is that way. Not very helpful at all most of the time... this stuff is really starting to annoy me.