This document discusses two special cases for factoring expressions: the difference of two squares and perfect square trinomials. It provides examples of factoring expressions using the difference of two squares formula a2 - b2 = (a + b)(a - b). It also covers recognizing and factoring perfect square trinomials using the forms (a + b)2 and (a - b)2. Exercises are provided to practice these factoring techniques.

2. To factor a perfect-square trinomialFrameworks: 10.P.5

3. Difference of Two Squares Let a2 and b2 represent areas of two squares. The orange region is the difference of the two squares Look at the picture on p. 259 b b a a

4. Difference of Two Squares a2 – b2 = (a + b)(a – b)

5. Factor a2 – 16

6. Factor y2– 36

7. Factor x2– 81

8. Factor 144x2– 49y2

9. Factor (x - 3)2– 25y2

10. Write a formula for the difference of the 2 squares: Then evaluate for r = 6 and t = 4.3 3r 2t

11. Factor 25x2 – 100y2

12. Factor (a + 4)2 – 64b2

13. Write a formula for the orange region: 4x y

14. Write a formula for the orange region: 5a 3c

15. Perfect Square Trinomials a2 + 2ab + b2 = (a + b)2 a2 - 2ab + b2 = (a - b)2 To factor a perfect square trinomial, you must first recognize its form: square of the first term +/- twice the product of the two terms square of the second term

16. Is 4x2 – 12x + 9 a perfect square trinomial?

17. Is 9x2+ 42x + 49 a perfect square trinomial?

18. Do p. 261 1-15