Differences of Squares
Any expression of the formis a difference of squares and factorises:
For example, ifthenand (note we always take the positive square root) so
Sometimes we need to factorise with any common factors before we can use the difference of squares factorisation.
Now putso thatand
The roots of the difference of squaresis the set of values offor whichThe roots are always equal in magnitude and opposite in sign. If an quadratic expression factorises into a difference of squares this is always the case. If we sketch this function, it is a quadratic graph with the line of symmetryand minimum at
The roots of the difference of squaresare x=-a and x=a. If we sketch this function, it is a quadratic graph with the line of symmetryand minimum atThis is a 'sad' curve, as opposed to the 'happy' curve above.
The above examples are quadratics, withterms but this need not be the case.