#### Oxygenthief

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The question is:

Solve (x^2 - 4) - 2(x -2)(x - 1) = 0 by factoring, do not expand first.

For the life of me I can't figure it out. Can anyone get me started?

Thanks!!

- Thread starter Oxygenthief
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The question is:

Solve (x^2 - 4) - 2(x -2)(x - 1) = 0 by factoring, do not expand first.

For the life of me I can't figure it out. Can anyone get me started?

Thanks!!

- Joined
- Jun 18, 2007

- Messages
- 18,149

Hint:

The question is:

Solve (x^2 - 4) - 2(x -2)(x - 1) = 0 by factoring, do not expand first.

For the life of me I can't figure it out. Can anyone get me started?

Thanks!!

(x^2 - 4 ) = (x^2 - 2

Now factor out the common factor.....

Subhotosh's hint:Solve (x^2 - 4) - 2(x -2)(x - 1) = 0 by factoring

(x^2 - 4 ) = (x^2 - 2^2 ) = (x - 2)(x + 2)

May be easier if you now let u = x - 2:

u(x + 2) - 2u(x - 1) = 0

Go to town with that, substitute back in to wrap up...

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This pattern is called "a difference of squares". Here's a short video showing its use, in a different situation.

https://www.youtube.com/watch?v=Wdb0V2hfYSU&feature=youtu.be

A difference of cubes, a sum of cubes, and perfect-square trinomials each have factoring patterns. Here's another video.

https://www.youtube.com/watch?v=1_kxLXFtqHg

These videos came from the following page (this site covers many beginning algebra topics, in addition to other subjects).

http://www.mathispower4u.com/algebra.php

You can also google keywords factoring patterns, to find other sites. :cool: