1. Difference of Squares December 3, 2014 Pages 42 – 43 in Notes

2. Warm-Up (Left Side – pg. 42) Write the perfect square numbers for 2 through 25 in the margin of your notes… (2 2 = ___, 3 2 = ___, etc…) Find the square root of the following expressions: 1.9 2.25 3.x 2 4.x 4

3. Objective solve quadratic equations and inequalities using graphs, tables, and algebraic methods.[8.D]

4. Essential Question What is the pattern for and what skills have I already learned that will help me with factoring the difference of squares?

5. What is this method for factoring? If there are only 2 terms, check for difference of squares (2 terms that you can take the square root of). [It has to be subtraction!] Factor like this… a 2 – b 2 = (a + b)(a – b) It will always factor into the sum times the difference of the square roots. *Always look for GCF first!

6. Example 1 x 2 – 9 Is there a GCF? No. Remember: a 2 – b 2 = (a + b)(a – b) … square roots are a = x and b = 3 So…factored form is… (x + 3)(x – 3)

7. Example 2 16x 2 – 4y 2 Is there a GCF? Yes, 4. So divide both terms: 4(4x 2 – y 2 ) Factor inside the ( ) using: a 2 – b 2 = (a + b)(a – b) … square roots are a = 2x and b = y So…factored form is… 4(2x + y)(2x – y) Don’t forget your GCF!!

8. Example 3 25x 2 – 49y 2 Is there a GCF? No. Factor using: a 2 – b 2 = (a + b)(a – b) … square roots are a = 5x and b = 7y So…factored form is… (5x + 7y)(5x – 7y)

9. Example 4 5x 2 – 12 Is there a GCF? No. 5 is not a perfect square so it cannot be factored. This is called a “prime polynomial.” Prime

10. Example 5 x 2 + 9 Addition of perfect squares can never be factored! Prime

11. Example 6 3x 2 + 27 Addition of perfect squares can never be factored unless there is a GCF! GCF is 3… Answer… 3(x 2 + 9)… Can’t factor further!

12. Example 7 x 4 – 16 Is there a GCF? No. Remember: a 2 – b 2 = (a + b)(a – b) … square roots are a = x 2 and b = 4 So…factored form is… (x 2 + 4)(x 2 – 4) But the second binomial will factor again using difference of squares… (x 2 + 4)(x + 2)(x – 2) Completely factored

13. Assignment – Difference of Squares 1.x 2 – 81 2.2x 2 – 8x 4 3.15x 2 – 225 4.x 2 – 25 5.8x 4 + 12x 2 6.14x 2 – 224y 2 7.x 2 + 4 8.9x 2 – 16y 2

14. Reflection What are the tips to remember on factoring the Difference of Squares?