# Simple Factoring Formulas

1. Jan 2, 2008

### nanoWatt

I don't really have a book to go by, and am going through examples online.

I'm finding that there are certain helpful formulas. Does anyone know of a collection of formulas that I can use.

For example, the difference of cubes: $$A^3 - B^3 = (A - B) (A^2 + AB + B^2)$$

It would be handy to have the sum of squares, sum of cubes, log, and formulas for working with e as well.

When going through factoring, the thing holding me back is I just don't have the formulas.

Thanks.

2. Jan 2, 2008

3. Jan 2, 2008

### Daniel Y.

Hi, nanoWatt. For factoring, it is common to have the three major factoring rules down by heart. Difference of Cubes (which you already have), Sum of Cubes $$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$, and Difference of Squares $$a^2 - b^2 = (a + b)(a - b)$$.

These are the three major factor-helpers you will see. However, these will not do for all things such as factoring quadratic equations. So it is good to form an intuitive knowledge of "how" the factors of cubes and squares work rather than *just* memorizing the 'formula' (such as learning how the middle terms of Difference of Squares 'drop out', rather than just memorizing where to put the a and b variables). This makes things like quadratic factoring easier to handle (or it did for me, anyway).

I don't know of any other factoring rules but those three basic one's, but those should be all you need if you're just doing Algebra (correct me if I'm wrong). Hope I helped. Good luck!

Last edited by a moderator: Jan 2, 2008
4. Jan 2, 2008

### symbolipoint

NanoWatt,
You say you have no textbook; just go buy a used introductory algebra book. You can develop factorization formulas on your own just by performing the multiplication steps on binomials and binomials & trinomials. You understand the distributive property? Then you can perform the multiplications. You should also check the Binomial Theorem (you'll find that in some intermediate algebra books, and also in College Algebra books).

5. Jan 2, 2008

### HallsofIvy

Staff Emeritus
In general, $A^n- B^n= (A-B)(A^{n-1}+ A^{n-2}B+ \cdot\cdot\cdot+ AB^{n-2}+ B^{n-1})$.

I'm not sure what you mean by "factoring formulas" involving logs or exponentials. One generally on "factors" polynomials.

I must say that learning "formulas" is far inferior to learning basic principles!
To factor something line $ax^2+ bx+ c$, you start with the knowledge that $(ex+ d)(fx+ g)= (ef)x^2+ (df+ eg)x+ dg$- that you need to factor a and c and then look at possible "df+eg" combinations of those factors.