Special Forms
There are a number of nice special forms of some polynomials which can make factoring easier for us on occasion. Following are the special forms.
a^{2 }+ 2ab + b^{2} = ( a + b )^{2}
a^{2} - 2ab + b^{2} = ( a - b )^{2}
a^{2} - b^{2} = ( a + b ) ( a - b )
a^{3} + b^{3} + ( a + b ) (a^{2} - ab + b^{2} )
a^{3} - b^{3} =(a - b ) (a^{2} + ab + b^{2} )
Let's take one examples with these.
Example 4 Factor following.
x^{2 }- 20 x + 100