Warm – up #4 Factor. 1. 6 𝑥 2 −3x 2. 𝑥 2 −25 3. 48𝑥 4 − 3𝑦 4

Warm – up #4 Solutions Factor. 1. 6 𝑥 2 −3x = 3x(2x – 1) 2. 𝑥 2 −25 = ( ) 2 − 2 = (x – 5)(x + 5) x 5

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

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

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

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

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

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 )

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

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)

Sum of Cubes 𝑥 3 + 𝑦 3 =(𝑥+𝑦)( 𝑥 2 −𝑥𝑦+ 𝑦 2 ) 3. 64𝑥 3 +125 = ( ) 3 + ( ) 3 = (4x + 5) 4. 𝑥 3 +216 𝑦 3 = (x+6y) 4x 5 (16 𝑥 2 - 20x + 25) x 6y ( 𝑥 2 - 6xy + 36 𝑦 2 )

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

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

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

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)

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)

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)

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)

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

Factor 15. 216𝑥 3 +64 = ( ) 3 + ( ) 3 = (6x + 4)(36 𝑥 2 - 24x+16) = 2(3x + 2)4(9 𝑥 2 −6𝑥+4) = 8(3x + 2)(9 𝑥 2 −6𝑥+4) OR from 216𝑥 3 +64  8(27 𝑥 3 +8) 6x 4 3x 2

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

Assignment: Factoring WS 2