1. Warm-up #23 (Monday, 10/26) Simplify (x+2)(3x – 4)
2. Simplify (x+2)( x 2 −3x−1)
3. Simplify −1 2 2

2. Homework (Monday, 10/26)
Factoring packet_pg 1 Lesson 2.06 worksheet

3. Lesson 2.10 Factoring a Difference of Squares

4. Factoring
3x+3 = 3(x+1)
3xy – 3x= 3x(y – 1)

5. Ex: Factor x(a + b) – 2(a + b)
Always ask first if there is common factor the terms share . . .
x(a + b) – 2(a + b)
Each term has factor (a + b)
 x(a + b) – 2(a + b)
= (a + b)( – ) x 2
(a + b)
(a + b)
 x(a + b) – 2(a + b) = (a + b)(x – 2)

6. Ex: Factor a(x – 2) + 2(2 – x)
As with the previous example, is there a common factor among the terms?
Well, kind of x – 2 is close to 2 - x Hum . . .
Recall: (-1)(x – 2) =
- x + 2 = 2 – x
 a(x – 2) + 2(2 – x) =
a(x – 2) + 2((-1)(x – 2))
= a(x – 2) + (– 2)(x – 2)
= a(x – 2) – 2(x – 2)
 a(x – 2) – 2(x – 2) =
(x – 2)( – ) a 2
(x – 2)
(x – 2)

7. Ex: Factor b(a – 7) – 3(7 – a) Common factor among the terms?
Well, kind of a – 7 is close to 7 - a
Recall: (-1)(a – 7) =
- a + 7 = 7 – a
 b(a – 7) – 3(7 – a) =
b(a – 7) – 3((-1)(a – 7))
= b(a – 7) + 3(a – 7)
= b(a – 7) +3(a – 7)
 b(a – 7) + 3(a – 7) =
(a – 7)( ) b 3
(a – 7)
(a – 7)

8. The difference of squares
For any numbers “a” and “b”, the following is an identity.
a2 – b2 = (a – b)(a + b)
Note: you can replace “a” and “b” by any number, variable, or expression
LIST ALL OF THE PERFECT SQUARES:

12. Ex: Factor x2 – 4
Notice the terms are both perfect squares
and we have a difference
 difference of squares
x2 = (x)2
4 = (2)2
 x2 – 4 = (x)2 – (2)2
= (x – 2)(x + 2)
a2 – b2
= (a – b)(a + b)
factors as

13. Example 1: 𝑥 2 −49
Example 2: 𝑥 2 −125

14. Ex: Factor 9p2 – 16
Notice the terms are both perfect squares
and we have a difference
 difference of squares
9p2 = (3p)2
16 = (4)2
 9a2 – 16 = (3p)2 – (4)2
= (3p – 4)(3p + 4)
a2 – b2
= (a – b)(a + b)
factors as

15. Example 1: 25𝑥 2 −16
Example 2: 15𝑥 2 −100

16. Ex: Factor y6 – 25
Notice the terms are both perfect squares
and we have a difference
 difference of squares
y6 = (y3)2
25 = (5)2
 y6 – 25 = (y3)2 – (5)2
= (y3 – 5)(y3 + 5)
a2 – b2
= (a – b)(a + b)
factors as

17. Example 1: 𝑚 8 −36
Example 2: 𝑥 6 −64

18. Ex: Factor 81 – x2y2
Notice the terms are both perfect squares
and we have a difference
 difference of squares
81 = (9)2
x2y2 = (xy)2
 81 – x2y2 = (9)2 – (xy)2
= (9 – xy)(9 + xy)
a2 – b2
= (a – b)(a + b)
factors as

19. Example 1: −36 + 𝑟 2 𝑚 2
Example 2: −125 + 𝑛 4 𝑥 2