Factoring (a+b)* (a-b) - (a+b) (a-b)*, (2a+1) (a+3) - (2a...

[ajade]

I am unsure how to slove these problems, could someone please give an example? I tried looking it up on Google but I couldn't find anything.

i'm not sure how to make a squared symbol so i'll use *. - how do i make a squared symbol?

1. (a+b)* (a-b) - (a+b) (a-b)*

2. (2a+1) (a+3) - (2a+1)(a-3)

3. 6m(3n-2m) (n+m) + 8m* (3n-2m) (n+m)

Thank you for the help!

 

[Loren]

Re: Factoring

Looks like you have an exercize on "grouping".

First you can indicate a power with the symbols "^2" for "squared", "^3" for "cubed", "^4" for "raised to the 4th power", etc.

If you use the "tex" icon at the top of this window and insert "x^2" between [tex ] and [/tex ] you get \(\displaystyle x^2\).

Now for your problems.

(a+b)* (a-b) - (a+b) (a-b)*

some people like to use a substitution process. After a few times doing this, you will be able to shorten it because you will see the common groups.

Let (a+b) be u.
Let (a-b) be v.

Your original expression becomes \(\displaystyle u^2v - uv^2\) which factors into uv(u-v).

Now make the substitution back getting (a+b)(a-b)((a+b)-(a-b)). Now, simplify getting (a+b)(a-b)(2b) or 2b(a+b)(a-b)

 

[mmm4444bot]

Re: Factoring

I tried looking it up on Google but I couldn't find anything.

I don't know what you were looking for at Google, but the Google results below may help.

First, you need to understand what "squared" means.

(a + b)^2 means that the expression (a + b) is being multiplied by itself.

(a + b)^2 = (a + b)(a + b)

You can multiply (a + b) times itself using four steps called the FOIL method.

Goggle results on search string "FOIL method multiply binomials"

After you learn the FOIL method, trying using it to multiply

(a + b)(a + b)

Here's a YOUTUBE video showing FOIL

Cheers,

~ Mark