Factoring - Difference of Squares and Perfect Square Trinomial Patterns
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 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.
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) = 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 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 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 - b)2 : b