Factoring formulas
Below are some factoring formulas that are used to factor some common math expressions
a
^{2}  b
^{2} = ( a  b ) × ( a + b )
a
^{4}  b
^{4} = ( a  b ) × ( a + b ) × ( a
^{2} + b
^{2} )
a
^{6}  b
^{6} = ( a  b ) × ( a + b ) × ( a
^{2}  ab + b
^{2} ) × ( a
^{2} + ab + b
^{2} )
a
^{8}  b
^{8} = ( a  b ) × ( a + b ) × ( a
^{2} + b
^{2} ) × ( a
^{4} + b
^{4} )
a
^{3} + b
^{3} = ( a + b ) × ( a
^{2}  ab + b
^{2} )
a
^{3}  b
^{3} = ( a  b ) × ( a
^{2} + ab + b
^{2} )
a
^{5}  b
^{5} = ( a  b ) × ( a
^{4} + a
^{3}b + a
^{2}b
^{2} + ab
^{3} + b
^{4} )
a
^{5} + b
^{5} = ( a + b ) × ( a
^{4}  a
^{3}b + a
^{2}b
^{2}  ab
^{3} + b
^{4} )
a
^{6}  b
^{6} = ( a  b ) × ( a
^{5} + a
^{4}b + a
^{3}b
^{2} + a
^{2}b
^{3} + ab
^{4} + b
^{5} )
a
^{6} + b
^{6} = ( a
^{2} + b
^{2} ) × ( a
^{4}  a
^{2}b
^{2} + b
^{4} )
a
^{7}  b
^{7} = ( a  b ) × ( a
^{6} + a
^{5}b + a
^{4}b
^{2} + a
^{3}b
^{3} + a
^{2}b
^{4} + ab
^{5} + b
^{6} )
a
^{4} + a
^{2}b
^{2} + b
^{4} = ( a
^{2} + ab + b
^{2} )× ( a
^{2}  ab + b
^{2} )
a
^{4} + 4b
^{4} = ( a
^{2} + 2ab + 2b
^{2} )× ( a
^{2}  2ab + 2b
^{2} )
Trick to factor a
^{n}  b
^{n} when n is an odd number. You cannot use this trick if n is even or to factor a
^{n} + b
^{n}
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 a
^{7}  b
^{7}, 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 ) × (a
^{6} + .................................................. + b
^{6})
Now here is the real tricky part
To get the next term, is a
^{5}b. 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 a
^{4}b
^{2}.
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

Jan 15, 18 11:55 AM
Learn how to solve radical equations with rational exponents and those with square roots
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.