# 3.3 NOTES Special Cases.docx - 3.3 NOTES Special Cases...

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3.3 NOTES Special Cases 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: = ( a + b )( a b ). - 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.