Factoring formulas


Below are some factoring formulas that are used to factor some common math expressions






a2 - b2 = ( a - b ) × ( a + b )


a4 - b4 = ( a - b ) × ( a + b ) × ( a2 + b2 )


a6 - b6 = ( a - b ) × ( a + b ) × ( a2 - ab + b2 ) × ( a2 + ab + b2 )


a8 - b8 = ( a - b ) × ( a + b ) × ( a2 + b2 ) × ( a4 + b4 )


a3 + b3 = ( a + b ) × ( a2 - ab + b2 )


a3 - b3 = ( a - b ) × ( a2 + ab + b2 )


a5 - b5 = ( a - b ) × ( a4 + a3b + a2b2 + ab3 + b4 )


a5 + b5 = ( a + b ) × ( a4 - a3b + a2b2 - ab3 + b4 )


a6 - b6 = ( a - b ) × ( a5 + a4b + a3b2 + a2b3 + ab4 + b5 )


a6 + b6 = ( a2 + b2 ) × ( a4 - a2b2 + b4 )


a7 - b7 = ( a - b ) × ( a6 + a5b + a4b2 + a3b3 + a2b4 + ab5 + b6 )


a4 + a2b2 + b4 = ( a2 + ab + b2 )× ( a2 - ab + b2 )


a4 + 4b4 = ( a2 + 2ab + 2b2 )× ( a2 - 2ab + 2b2 )




Trick to factor an - bn when n is an odd number. You cannot use this trick if n is even or to factor an + bn


First start by writing ( a - b ) × ( ..................................................)


Then, fill in the parenthesis on the right

To do this, follow this guideline.

Subtract 1 from n. For example, if n = 7 as in a7 - b7, subtract 1 from 7 to get 6.


The first term is always going to be the first variable that is a raised to the power of 6


The first term is always going to be the second variable that is b raised to the power of 6


The operation inside is always a plus

So it is going to look like ( a - b ) × (a6 + .................................................. + b6)


Now here is the real tricky part

To get the next term, is a5b. This is done by subtracting 1 from 6 and incorporating the other variable

Now all you have to do is to keep subtracting 1 to the exponent of a and adding 1 to the exponent of b as shown below

The next term will be a4b2.

Do this until the variable a disappears and you will end up with the answer already shown above

Have a question about these factoring formulas? Contact me







Recent Articles

  1. Linear Parent Function

    Nov 20, 17 11:18 AM

    What is a linear parent function? Crystal clear explanation.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest





Recent Lessons

  1. Linear Parent Function

    Nov 20, 17 11:18 AM

    What is a linear parent function? Crystal clear explanation.

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz