SOLUTION: Can some one please help explain these in detail? I am so lost. Thank you Factor completely: 9x^2 -16y^2 3x^2-2x-8 3x^2 + 12x +12 Thanks again for all your help!

Question 35705: Can some one please help explain these in detail? I am so lost. Thank you
Factor completely:
9x^2 -16y^2
3x^2-2x-8
3x^2 + 12x +12
Thanks again for all your help!

Thank you
Found 2 solutions by rapaljer, Earlsdon:
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
From the variety of factoring problems you have here, you probably need to visit my website by clicking on my user name "rapaljer" anywhere in algebra.com. Then go to Basic Algebra, and look for "Samples from Basic Algebra: One Step at a Time". Click on Chapter 2, and see all the sections on factoring. This contains all the explanation, examples, exercises, and answers and it's all FREE. Check it out. Many if not all of these are also Lesson Plans on algebra.com if you want to look for them here.

Now, is a difference of squares.

Secondly, comes from a section that I call "Advanced Trinomial Factoring". This is a hard one for most people. You have to start off with a which can only be factored into 3x*x.

The last times last must come out to a -8, so I would try a 4 times 2 or a 2 times 4 combination. By trial and error (see my website for details!), it turns out that the 4 should come first and the 2 should go second like this:

The outer times outer is -6x and the inner times inner is 4x for a total of -2x, which checks for the middle term.

is a problem that turns out to be a perfect square trinomial (in my website, this is in with the difference of squares section).
You must first take out the common factor which is 3:

Next, factor the trinomial:

R^2 at SCC

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Factor:
1) This is the difference of two squares and can be factored as follows:
Applying this to your problem:
=
2)
The factors of 3x^2 are:(3x)(x)
The factors of -8 are: (-1)(8) or (-2)(4) or (2)(-4)
Try =
The factors are:
3)
The factors of 3x are:(3x)(x)
The factor of 12 are: (1)(12) or (2)(6) or (3)(4)
Try =
The factors are:
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