Special Factoring Patterns

Students will be able to recognize and use special factoring patterns

FHS Polynomials 2

Difference of Squares• The difference of squares is a perfect

square minus a perfect square, such as a2 – b2

• This can be factored into the sum and the difference of the two square roots, or

(a + b)(a – b) • So we can factor any polynomial that fits

this pattern as a2 – b2 = (a + b)(a – b)

FHS Polynomials 3

Perfect Square Trinomial

The other special factoring pattern is called the perfect square trinomial. Every binomial multiplied by itself fits this pattern.

1. First term is a perfect square.2. Last term is a perfect square.3. Middle term is formed by doubling the

product of the first and last term square roots.

4. Example: 22 or 2 ba ab

FHS Polynomials 4

ExamplesFind the binomial factors for the following, if

possible:1. 4.

2. 5.

3. 6.

2x 10x 25

2 24x 12xy 9y

29x 36

249x 28x 2

2 281x 8y

2 264x 48xy 9y

2x 5

22x 3y

3x 6 3x 6 28x 3y

Cannot be factoredCannot be factored