3.3 NOTES Special Cases
- Study the equation below. Is there anything noticeable about the terms x2 and 9?
y = x2 − 9
- Both terms are perfect squares! In fact, the expression has special qualities that make it easier to factor. -
- This lesson explores how to identify and factor two special kinds of quadratic expressions: the
difference of squares and perfect square trinomials.
- A key component to understanding these special expressions is being able to identify perfect squares.
DIFFERENCE OF SQUARES:
- difference of Squares:
An expression that contains two perfect squares with one subtracted from the
other. A difference of squares can always be factored as follows:
- perfect squares:
Numbers that are the square of an integer. In other words, a perfect square can be
expressed as an integer multiplied by itself. (Sometimes this definition is extended to include the squares
of rational numbers.) A perfect square can also include a variable. In this case, the variable term must be
able to be expressed as a variable raised to a power multiplied by itself.
- Let's take a look at x2 - 9. You already noticed that the terms, x2 and 9, are perfect squares.
- Another important property of this expression is the operation.
- In fact, x2 - 9 is an example of a quadratic expression called a difference of squares.