Useful expansions form quadratic equation

   in special form

The left hand side comes from a root of quadratic function . Since , we can regard a=1, b=x, and c=-1 as in . Recall that the roots are . The right hand side is derived from

   in special form

The left hand side comes from a root of quadratic function . Since , we can regard a=1, b=1, and c=-x as in . The right hand side is derived from

   in special form

The left hand side comes from a root of quadratic function . Since , we can regard a=1, b=x, and c=-x as in . The right hand side is derived from