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

2. Warm-Up (Left Side – pg. 42)
Find the square root of the following expressions: 9 25 x2 x4

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

4. Essential Question
What skills that I have already learned will help me with finding 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).
Factor like this…
a2 – b2 = (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 x2 – 9 Is there a GCF? Remember: a2 – b2 = (a + b)(a – b)
No.
Remember: a2 – b2 = (a + b)(a – b)
a = x and b = 3
So…factored form is…
(x + 3)(x – 3)

7. Example 2 16x2 – 4y2 Is there a GCF?
Yes, 4. So divide both terms: 4(4x2 – y2)
Factor inside the ( ) using: a2 – b2 = (a + b)(a – b)
a = 2x and b = y
So…factored form is…
4(2x + y)(2x – y)

8. Example 3 25x2 – 49y2 Is there a GCF?
No.
Factor using: a2 – b2 = (a + b)(a – b)
a = 5x and b = 7y
So…factored form is…
(5x + 7y)(5x – 7y)

9. Example 4 5x2 – 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 x2 + 9 Addition of perfect squares can never be factored!
Prime

11. Example 6 x4 – 16 Is there a GCF? Remember: a2 – b2 = (a + b)(a – b)
No.
Remember: a2 – b2 = (a + b)(a – b)
a = x2 and b = 4
So…factored form is…
(x2 + 4)(x2 – 4)
But the second binomial will factor again…
(x2 + 4)(x + 2)(x – 2)
Completely factored

12. Assignment – Difference of Squares
x2 – 81
2x2 – 8x4
15x2 – 225
x2 – 25
8x4 + 12x2
14x2 – 224y2
x2 + 4
9x2 – 16y2

13. Reflection