Originally Posted by

**Diamondlance** I was tutoring a student in Algebra today, and came across an interesting factoring problem. The student had just finished a unit on factoring techniques (sum/difference of cubes, difference of squares, trinomials, etc.) Where I was tutoring the common rules of thumb taught are, after factoring the gcf, for binomials check difference of squares, etc.; for trinomials try factoring by finding two appropriate binomials in the usual way, and for 4-termed polynomials try grouping. This example goes against these rules of thumb taught, so I was wondering, although I know how to do this problem, if anyone here knows a better way to explain how to do it. The problem was to factor

$\displaystyle x^2-6x-y^2+9$

I told the student that, to better see what to do, rewrite as

$\displaystyle x^2-6x+9-y^2$

and factor the trinomial on the left

$\displaystyle (x-3)^2-y^2$

resulting in a difference of two squares.

$\displaystyle [(x-3)-y][(x-3)+y]$

Any advice on how to get an average algebra student to see the appropriate first steps?