1. Warm – up #4
Factor 𝑥 2 −3x 2. 𝑥 2 − 𝑥 4 − 3𝑦 4

2. Warm – up #4 Solutions
Factor 𝑥 2 −3x = 3x(2x – 1) 2. 𝑥 2 −25 = ( ) 2 − 2 = (x – 5)(x + 5) x 5

3. Warm – up #4 Solutions
3. 48𝑥 4 − 3𝑦 4 = 3(16 𝑥 4 − 𝑦 4 ) = ( ) 2 − 2 = 3(4 𝑥 2 − 𝑦 2 )(4 𝑥 2 + 𝑦 2 ) = 3(2x – y)(2x + y)(4 𝑥 2 + 𝑦 2 )
4 𝑥 2
𝑦 2 2x y

4. Homework Log Fri 11/6 Lesson 4 – 4 Learning Objective:
To factor difference and sum of cubes & by grouping
Hw: Factoring WS 2

5. 11/6/15 Lesson 4 – 4 Factoring Day 2
Algebra II

6. Learning Objective To factor difference of cubes
To factor sum of cubes
To factor by grouping

7. Factoring
Difference of Squares 𝑥 2 − 𝑦 2 =(𝑥−𝑦)(𝑥+𝑦) Sum of Squares 𝑥 2 + 𝑦 2 = Can’t be factored!

8. Factoring
Difference of Cubes 𝑥 3 − 𝑦 3 =(𝑥−𝑦)( 𝑥 2 +𝑥𝑦+ 𝑦 2 ) Sum of Cubes 𝑥 3 + 𝑦 3 =(𝑥+𝑦)( 𝑥 2 −𝑥𝑦+ 𝑦 2 )

9. Difference & Sum of Cube “Song”
Pull out the cube roots
Square the first term
Change the Sign
First times the second term
Plus the last term squared

10. Difference of Cubes
𝑥 3 − 𝑦 3 =(𝑥−𝑦)( 𝑥 2 +𝑥𝑦+ 𝑦 2 ) 1. 8𝑥 3 −1 = ( ) 3 − ( ) 3 = (2x – 1) 2. 27𝑥 3 −8 = (3x – 2) 2x 1
(4 𝑥 2
+ 2x
+ 1) 3x 2
(9 𝑥 2
+ 6x
+ 4)

11. Sum of Cubes
𝑥 3 + 𝑦 3 =(𝑥+𝑦)( 𝑥 2 −𝑥𝑦+ 𝑦 2 ) 3. 64𝑥 = ( ) 3 + ( ) 3 = (4x + 5) 4. 𝑥 𝑦 3 = (x+6y) 4x 5
(16 𝑥 2
- 20x
+ 25) x 6y
( 𝑥 2
- 6xy
+ 36 𝑦 2 )

12. Sum of Cubes
5. 𝑥 9 +1 = ( ) 3 + ( ) 3 = ( 𝑥 3 + 1)( 𝑥 6 - 𝑥 3 +1) = (x + 1)( 𝑥 2 −𝑥+1)( 𝑥 6 - 𝑥 3 +1)
𝑥 3 1 x 1

13. Factor By Grouping Factor By Grouping
Mainly used when there are 4 terms
Group the first two terms & the last two terms
Factor from each group
“Combine” like terms

14. Review Factoring
Factor 6. 4𝑥 2 𝑦−6𝑥 = 2x(2xy – 3) 7. 𝑥 2 −𝑥 = x(x – 1)

15. Factor by Grouping 8. 3𝑥 2 +2𝑥𝑦+10𝑦+15𝑥 = x(3x + 2y)+5(2y + 3x) =
9. 7𝑥 2 𝑦−6 𝑥 2 −7𝑦+6
= 𝑥 2 (7y – 6)- 1(7y - 6) =
(7y – 6)
( 𝑥 2 −1)
= (7y – 6)(x + 1)(x – 1)

16. Factor by Grouping
10. 32ax + 12bx – 48ay – 18by = 2(16ax + 6bx – 24ay - 9by) = 2(2x(8a + 3b) – 3y(8a + 3b)) = 2
(8a + 3b)
(2x – 3y)

17. Factor by Grouping
11. 30ac + 80bd + 40ad + 60bc = 10(3ac + 8bd + 4ad + 6bc) = 10(3ac + 4ad + 8bd + 6bc) = 10(a(3c + 4d) + 2b(4d + 3c)) = 10
(3c + 4d)
(a + 2b)

18. Factor 12. 𝑥 3 −3 𝑥 2 +𝑥−3 = 𝑥 2 (x – 3)+1(x – 3) = (x – 3) ( 𝑥 2 + 1)
13. 2𝑥 3 −16 𝑥 2 −8𝑥+64
= 2( 𝑥 3 −8 𝑥 2 −4𝑥+32)
= 2( 𝑥 2 𝑥−8 −4(𝑥−8))
= 2
(x – 8)
( 𝑥 2 −4)
= 2(x – 8)(x + 2)(x – 2)

19. Factor
14. 8𝑥 3 −8 = 8( 𝑥 3 −1) = ( ) 3 − ( ) 3 = 8(x – 1)( 𝑥 2 + x + 1) x 1

20. Factor
𝑥 = ( ) 3 + ( ) 3 = (6x + 4)(36 𝑥 x+16) = 2(3x + 2)4(9 𝑥 2 −6𝑥+4) = 8(3x + 2)(9 𝑥 2 −6𝑥+4) OR from 216𝑥  8(27 𝑥 3 +8) 6x 4 3x 2

21. Ticket Out the Door Factor 54𝑥 3 + 16𝑦 3 54𝑥 3 − 16𝑦 3
What’s the difference in your answers?

22. Assignment: Factoring WS 2