Factoring A Difference Of Two Squares

Once students are familiar with the idea of factoring, there are shortcuts to the FOIL method of quadratic equation factoring.  One of these is factoring a difference of two squares.  A difference of two squares means that we have a monomial multiplied by another monomial to give us a quadratic function where one monomial is a conjugate pair of the other and the middle term in the quadratic form of an equation disappears.

A quadratic equation is represented by ax+bx+c, when the "bx" term disappears, we have a difference of two squares.

Example:

(x-3)*(x+3), here (x+3) is a conjugate pair of (x-3), and here is where we get a difference of two squares.

(x-3)(x+3), using the FOIL  method, is:

(x)(x)+(x)(3)+(-3)(x)+(-3)(3)=
x+3x-3x-9
x-9.  

Here, we see that since the middle term disappeared, we see that (x-3)(x+3) is simply x-3, the two squares being x and 3, which is why it is called the difference of two squares.

Of course, the same thing would result if we were doing (x+3)(x-3) since multiplication is commutative.

Now, to give more examples:

(x+4)(x-4)= (x-4)=(x-16)

(x+9)(x-9)=(x-9)=(x-81)