How to Factor a Difference of Squares (Mathematics Lesson)
What Is the Difference of Squares?The difference of squares is a special type of quadratic equation:
How to Factor a Difference of SquaresA difference of squares always factors to a simple expression:
Expand the brackets using the FOIL method to show this is the case (see Note).
A Real Example of Factoring a Difference of SquaresQuestion: Factor and solve the difference of squares below:
Is the constant term, 9, a square number? Yes.
9 = 32
Compare a2 - b2 with x2 - 9.
a = x, b = 3
Equate the quadratic equation to 0 and solve for x. Each bracket in the factored equation can be equated to 0 in turn and solved for x
The solution to the quadratic equation x2 - 9 = 0 is x = -3 or x = 3.
Another Real Example of How to Factor a Difference of SquaresThe slider below shows another real example of how to factor a difference of squares.
NoteWHAT'S IN A NAME?
A difference of squares is so called because it is a difference (the result of subtraction) of two square numbers.
WHY THIS FACTORING WORKSFactoring is the opposite of expanding two brackets using the FOIL method.
Let's go backwards. Start with the difference of squares factored into two brackets:
Expand the brackets using the FOIL method:
...which is a difference of squares!