# Factoring by grouping

• Jul 7th 2009, 12:48 PM
allyourbass2212
Factoring by grouping
Just a basic question, but how are you supposed to know an expression can be factored by grouping if the instructions do not point it out to you?

For instance the expression $6xy^2+4xy+9xy+6x$ may be factored by grouping, however at first glance im almost certain I would miss it unless the instructions specifically stated "factor by grouping".

Many thanks for any tips.
• Jul 7th 2009, 12:52 PM
Prove It
Quote:

Originally Posted by allyourbass2212
Just a basic question, but how are you supposed to know an expression can be factored by grouping if the instructions do not point it out to you?

For instance the expression $6xy^2+4xy+9xy+6x$ may be factored by grouping, however at first glance im almost certain I would miss it unless the instructions specifically stated "factor by grouping".

Many thanks for any tips.

Unfortunately there is not any definitive way to know whether an expression can be factorised by grouping. It just takes some experience.
• Jul 7th 2009, 01:43 PM
Soroban
Hello, allyourbass2212!

My rule is: If it has four or more terms, try "grouping".

Sometimes, we must rearrange the terms,
. . so some imagination may be required.

. . $\begin{array}{cc}\text{Example:} & x^2 + 3x + y^2 + 3y + 2xy \\ \\

\text{Rearrange:} &\underbrace{x^2 + 2xy + y^2} + \underbrace{3x + 3y} \\ \\

\text{Factor:} & (x+y)^2 + 3(x+y) \\ \\

\text{Factor:} & (x+y)(x+y+3) \end{array}$

• Jul 8th 2009, 05:02 AM
HallsofIvy
The important word in what Soroban said is "try"! Like so many other things in mathematics (or life for that matter!) we don't know what will work so we try different things until one works.
• Jul 8th 2009, 07:54 AM
allyourbass2212
Thank you everyone for your insight into the matter!