Factoring Difference of Squares and Perfect Square Trinomial

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Factoring - Difference of Squares and Perfect Square Trinomial Patterns

Factoring - Difference of Squares and Perfect Square Trinomial Patterns

What numbers are Perfect Squares? Squares Perfect Squares 1 4 9 16 25 36

What numbers are Perfect Squares? Squares 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

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? x 2 – 9 = (x + 3)(x – 3) The sum of squares will not factor a 2+b 2

Using FOIL we find the product of two binomials.

Using FOIL we find the product of two binomials.

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

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

Conditions for Difference of Squares Must be a binomial with subtraction. First term must be a perfect square. (x)(x) = x 2 Second term must be a perfect square (6)(6) = 36

Check for GCF. Sometimes it is necessary to remove the GCF before it can

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

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

Difference of Squares You Try

Factoring a perfect square trinomial in the form:

Factoring a perfect square trinomial in the form:

Perfect Square Trinomials can be factored just like other trinomials (guess and check), but

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 Does the middle term fit the pattern, 2 ab? Yes, the factors are

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

a Does the middle term fit the pattern, 2 ab? Yes, the factors are

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