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} )
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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