Factoring formulas
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Below are some factoring formulas that are used to factor some common math expressions.
a2 - b2 = ( a - b ) × ( a + b )4 - b4 = ( a - b ) × ( a + b ) × ( a2 + b2 )6 - b6 = ( a - b ) × ( a + b ) × ( a2 - ab + b2 ) × ( a2 + ab + b2 )8 - b8 = ( a - b ) × ( a + b ) × ( a2 + b2 ) × ( a4 + b4 )3 + b3 = ( a + b ) × ( a2 - ab + b2 )3 - b3 = ( a - b ) × ( a2 + ab + b2 )5 - b5 = ( a - b ) × ( a4 + a3 b + a2 b2 + ab3 + b4 )5 + b5 = ( a + b ) × ( a4 - a3 b + a2 b2 - ab3 + b4 )6 - b6 = ( a - b ) × ( a5 + a4 b + a3 b2 + a2 b3 + ab4 + b5 )6 + b6 = ( a2 + b2 ) × ( a4 - a2 b2 + b4 )7 - b7 = ( a - b ) × ( a6 + a5 b + a4 b2 + a3 b3 + a2 b4 + ab5 + b6 )4 + a2 b2 + b4 = ( a2 + ab + b2 ) × ( a2 - ab + b2 )4 + 4b4 = ( a2 + 2ab + 2b2 ) × ( a2 - 2ab + 2b2 )
Factoring formulas trick
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 last 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.
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