What numbers are Perfect Squares?

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Presentation transcript:

Factoring - Difference of Squares and Perfect Square Trinomial Patterns

What numbers are Perfect Squares? 1 4 9 16 25 36 49 64 81 100

Factoring: Difference of Squares Count the number of terms. Is it a binomial? Is the first term a perfect square? Is the last term a perfect square? Is it, or could it be, a subtraction of two perfect squares? x2 – 9 = (x + 3)(x – 3) The sum of squares will not factor a2+b2

Using FOIL we find the product of two binomials.

Rewrite the polynomial as the product of a sum and a difference.

Conditions for Difference of Squares Must be a binomial with subtraction. First term must be a perfect square. (x)(x) = x2 Second term must be a perfect square (6)(6) = 36

Check for GCF. Sometimes it is necessary to remove the GCF before it can be factored more completely.

Removing a GCF of -1. In some cases removing a GCF of negative one will result in the difference of squares.

Difference of Squares You Try

Factoring a perfect square trinomial in the form:

Perfect Square Trinomials can be factored just like other trinomials (guess and check), but if you recognize the perfect squares pattern, follow the formula!

a b Does the middle term fit the pattern, 2ab? Yes, the factors are (a + b)2 :

a b Does the middle term fit the pattern, 2ab? Yes, the factors are (a - b)2 :