Simplifying Algebraic Factoring: Identifying Patterns and Formulas

[JoshHolloway]

In another thread someone showed me this identity:
$$1+x+y^{2}+xy^{2}=(1+x)(1+y^{2})$$

How does one recognize that the Left side of this equation can be factored into the form on the right? Is there some formula, or do you just have to memorize these kind?

 

[TD]

In another thread someone showed me this identity:
$$1+x+y^{2}+xy^{2}=(1+x)(1+y^{2})$$

How does one recognize that the Left side of this equation can be factored into the form on the right? Is there some formula, or do you just have to memorize these kind?

In the last two terms, you see a common factor y². Pulling it out would give:

1+x+y²(1+x)

Now you see the (1+x) twice, factoring it gives:

(1+x)(1+y²)

 

[JoshHolloway]

Sweet. Thanks a lot man. You have really brightend me day!

 

[TD]

Sweet. Thanks a lot man. You have really brightend me day!

You're welcome

 

[arildno]

It is not as much about memorizing stuff, as it is about a willingness to play about with symbols (in a valid manner) to see what is "possible", or leads to simplifications.

Gradually, by doing this, you will develop a knack to recognize patterns like the given one at a glance.