1. 6.2 Difference of 2 Squares
Goal: To be able to recognize and completely factor the difference of two squares
Remember to factor out a common factor before you see if it is the difference of two squares or not!!!

2. 9 is a Perfect Square because 3 • 3 = 9
9 is a Perfect Square because 3 • 3 = 9. Can you find the other perfect squares? 12 9 10 16 x2 x5 x6 x9

3. A “term” (such as 9x4) is a Perfect Square if:
The coefficient (9) is a perfect square, and
The variable has an even number for an exponent.
To take the square of an even exponent divide by 2

4. Is this term a perfect Square?
4y6 = (2y3)(2y3)
4y6
4y9
16y1
8y10
25y10
9y156
1y6
= 3y78 • 3y78

5. Are both terms perfect Squares?
4y6 – 9x2
y6 – 9x8
8y6 – 25x2
9y6 – 4x2y8

6. Factoring the difference of two squares
(A + B)(A – B) = A2 – B2
A2 – B2 = (A + B)(A – B)
= (y + 3)(y – 3)
y2 – 9
m2 – 64
= (m + 8)(m – 8)

7. Factor:
9x2 – 25
( )( ) 5 3x

8. Factor:
y6 – 9x2
(y3 + 3x)(y3 - 3x)

9. Factor:
4y6 – 9x2
(2y3 + 3x)(2y3 - 3x)

10. Three more “notes”
(y2 + 25) cannot be factored.
Factor out any common terms first, then continue.
20y6 – 5  5(4y6 – 1)
Factor completely. 81x4 – 1
 (9x2 + 1) (9x2 – 1)
(9x² +1) (3x + 1) (3x - 1)

11. Factor completely: 25x4 - 9

12. Factor completely: 32x2 – 50y2
2(4x + 5y) (4x - 5y)

13. Factor completely: 16x4 – y8
(4x2 + y4) (4x2 – y4)
(4x2 + y4)(2x + y2) (2x – y2)

14. Factor completely: 9x4 + 36
Cannot be factored

15. Closing.. To factor the difference of 2 squares:
Factor out a common factor
If there is subtraction of two squares, take the square root of each one + and one –
Check to see if the - of your final answer is not another difference of two squares.

16. Assignment: Page 268 10-48 even