Useful expansions form quadratic equation(with alternate signs)

   in special form

The left hand side comes from a root of quadratic function. Here, we can regard a=x, b=x²-2, and c=-x 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 where we can regard a=1, b=-1-2*x, 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 where we can regard a=1, b=x-2, and c=-x as in . The right hand side is derived from

where both positive and negative signs appear by turns.