Factoring Cubes and Factoring by Grouping

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Presentation transcript:

Factoring Cubes and Factoring by Grouping Student Learning Goal: Students will be able to factor perfect cubes and be able to factor by grouping. Homework: Worksheet

Review of Factoring Special Cases: (x + 5) (x -5) = (2x – 7) (2x + 7) = ( 𝑥+4) 2 = 6𝑥 −1 2 = Special Cases Formula: 𝑎+𝑏 𝑎 −𝑏 = 𝑎 2 - 𝑏 2 𝑎+𝑏 2 = 𝑎 2 + 2ab + 𝑏 2 “Square Double Square” 𝑎−𝑏 2 = 𝑎 2 - 2ab + 𝑏 2 “Square Double Square”

Factoring Cubes: 𝑎 3 + 𝑏 3 =( 𝑎+𝑏)( 𝑎 2 −2𝑎𝑏+ 𝑏 2 ) (S. M. O. S Factoring Cubes: 𝑎 3 + 𝑏 3 =( 𝑎+𝑏)( 𝑎 2 −2𝑎𝑏+ 𝑏 2 ) (S.M.O.S. = “Square-multiply-opposite-square” ) 𝑎 3 − 𝑏 3 =(𝑎 −𝑏)( 𝑎 2 +2𝑎𝑏+ 𝑏 2 ) Example 1: Multiply 𝑥 3 +8 = 𝑥 3 −64= 8𝑥 3 +125=

Factoring by Grouping: 𝑥 3 + 5𝑥 2 −4𝑥 −20 𝑥 3 − 2𝑥 2 −9𝑥+18

Factor Each Polynomial Completely 𝑎 3 +27 3𝑦 3 + 𝑦 2 +9𝑦+3 16𝑛 4 −625 6𝑥 5 − 750𝑧 2