1. 7.7 Perfect Squares and Factoring CORD Math Mrs. Spitz Fall 2006

2. Objective Identify and factor perfect square trinomials.

3. Assignment Pg. 283 #4-42 all

4. Introduction Numbers such as 1, 4, 9 and 16 are called perfect squares since they can be expressed as the square of an integer. Products of the form (a + b) 2 and (a – b) 2 are also called perfect squares, and the expansions of these products are called perfect square trinomials.

5. Perfect Square Trinomials

6. These patterns can be used to help you factor trinomials. Finding a Product

7. These patterns can be used to help you factor trinomials. Factoring

8. These patterns can be used to help you factor trinomials. Finding a Product

9. These patterns can be used to help you factor trinomials. Factoring

10. Can it be factored? To determine whether a trinomial can be factored by using these patterns, you must first decide if it is a perfect square trinomial. In other words, you must determine whether it can be written in the form

11. Example 1: Determine whether x 2 + 22x +121 is a perfect square trinomial. If so, factor it. a.Is the first term a perfect square? To determine whether x 2 + 22x + 121 is a perfect square trinomial, answer each question. YES b.Is the last term a perfect square? c.Is the middle term 2(a)(b)? x 2 (x) 2 121 (11) 2 22x 2(x)(11)

12. So, x 2 + 22x + 121 is a perfect square trinomial. It can be factored as follow:

13. Example 2: Determine whether 16a 2 + 81 – 72a is a perfect square trinomial. If so, factor it. a.Is the first term a perfect square? First arrange the terms of 16a 2 + 81 + 72a, so the powers of a are in descending order. YES b.Is the last term a perfect square? c.Is the middle term 2(a)(b)? 16a 2 (4a) 2 81 (9) 2 72a 2(4a)(9)

14. So, 16a 2 – 72a + 81 is a perfect square trinomial. It can be factored as follow:

15. Example 3: Determine whether 9p 2 - 56p + 49 is a perfect square trinomial. If so, factor it. a.Is the first term a perfect square? Follow the steps. YES NO b.Is the last term a perfect square? c.Is the middle term 2(a)(b)? d.? 9p 2 (3p) 2 49 (7) 2 56p 2(3p)(7) 9p 2 - 56p + 49 is NOT a perfect square trinomial.

16. So, 16a 2 – 72a + 81 is a perfect square trinomial. It can be factored as follow:

17. Example 4: Is it possible for 9x 2 + 12xy + 4y 2 is a perfect square trinomial? If so, what is the measure of each side of the square? a.Is the first term a perfect square? Follow the steps. YES NO b.Is the last term a perfect square? c.Is the middle term 2(a)(b)? 9x 2 (3x) 2 4y 2 (2y) 2 12xy 2(3x)(47)

18. So, Yes. 9x 2 +12xy + 4y 2 is a perfect square trinomial. Each side is (3x + 2y).