Factoring

[malelia123]

Having some trouble with my basic Math.
Factoring, can someone explain how to factor the following:

(x^2-1)


(4a^2-1)


Here are my tries:

x(x-1)


2a(2a-1)


I'm trying to figure out adding and subtracting rational expressions but I think I'm missing some basics.

 

[JeffM]

Having some trouble with my basic Math.
Factoring, can someone explain how to factor the following:

(x^2-1)


(4a^2-1)


Here are my tries:

x(x-1) \(\displaystyle = x^2 - x \ne x^2 - 1.\)


2a(2a-1) \(\displaystyle = 4a^2 - 2a \ne 4a^2 - 1.\)

Check your work.

I'm trying to figure out adding and subtracting rational expressions but I think I'm missing some basics.

You are missing one of the basic basics: difference of two squares

\(\displaystyle u^2 - v^2 = (u - v)(u + v).\)

Now try applying that to your problems

 

[HallsofIvy]

Having some trouble with my basic Math.
Factoring, can someone explain how to factor the following:

(x^2-1)


(4a^2-1)


Here are my tries:

x(x-1)


2a(2a-1)

JeffM has already answered your question I just want to point out that you could have seen immediately that your tries are wrong: by the "distributive law" x(x- 1)= x(x)- x(1)= x^2- x, not x^2- 1, and 2a(2a- 1)= 4a^2- 2a, not 4a^2- 1.