1. 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 $\displaystyle 6xy^2+4xy+9xy+6x$ 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.

2. 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 $\displaystyle 6xy^2+4xy+9xy+6x$ 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.

3. 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.

. . $\displaystyle \begin{array}{cc}\text{Example:} & x^2 + 3x + y^2 + 3y + 2xy \\ \\ \text{Rearrange:} &\underbrace{x^2 + 2xy + y^2} + \underbrace{3x + 3y} \\ \\ \text{Factor:} & (x+y)^2 + 3(x+y) \\ \\ \text{Factor:} & (x+y)(x+y+3) \end{array}$

4. 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.

5. Thank you everyone for your insight into the matter!