FACTORING SPECIAL

PRODUCTS

Math Notebook

Review

Find the product of (m+2) (m-2)

Find the product of (2y-3)^2

Perfect Square Polynomials First Term is a perfect square

Last Term is a perfect square

Middle Term: Multiply the square root of the first and last terms, then double it

Question: is x^2 + 12x + 36 a perfect square polynomial?

Difference of Two Square Patterns

Algebra: a^2 – b^2 = (a+b) (a-b)

Example: 2x^2 -9 = (2x)^2 -3^2 = (2x+3) (2x-3)

Examples

Factor the polynomial Factored Form

1) y^2 -16 = y^2 -4^2

2) 25m^2 -36 = (5m)^2 -6^2

3) x^2 - 49y^2 = ?

(y+4) (y-4)

(5m +6) (5m-6)

(x+7y) ( )

Example

Factor the polynomial Steps

8 – 18n^2

2 ( 4 – 9n^2)

2 ( (2)^2 – (3n)^2

2 (2+3n)(2-3n)

Factor out the greatest common factor

Write 4 – 9n^2 as a^2 -b^2

Perfect Square Trinomials

Example

The pattern for finding the square of the binomial gives you the pattern for factoring trinomials of the form:

A^2 -2ab+b^2

A^2 +2ab+b^2

Examples