A3 4.1e To Factor the Sum of Two Cubes And the Difference of Two Cubes 11-9-18 A3 4.1e To Factor the Sum of Two Cubes And the Difference of Two Cubes

Active Learning Assignment? 4

FACTORING RULES! Always see if you can factor out a common term. COUNT TERMS!!! TWO TERMS: a.) Difference of Two Squares: a2 – b2 = (a + b) (a – b) b.) Sum of Two Cubes: a3 + b3 = (a + b) (a2 – ab + b2) c.) Difference of Two Cubes: a3 – b3 = (a – b) (a2 + ab + b2)

Also remember that perfect cube powers are multiples of 3. Extra: Use your calculator to find roots: 1. 2. Power Root (If you want the 3rd root, do this first.) (Use parentheses!) (Above the ^ on TI 30-X) Also remember that perfect cube powers are multiples of 3. 10 4

Ex: 1. x3 + 8 Try: 2. x6 + y6 a = x & b = 2 a = x2 & b = y2 LESSON: Remember, you have a list of perfect cubes on your cube sheet. The formulas are: Sum of Two Cubes: a3 + b3 = (a + b) (a2 – ab + b2) Difference of Two Cubes: a3 – b3 = (a – b) (a2 + ab + b2) FIRST, determine what “a” and “b” are. Ex: 1. x3 + 8 Try: 2. x6 + y6 a = x & b = 2 a = x2 & b = y2 (a + b) (a2 – ab + b2) (a + b) (a2 – ab + b2) (x + 2) (x2 – 2x + 4) (x2 + y2) (x4 – x2 y2 + y4)

Ex: 3. x6 – 125 Try: 4. 8x3 – y9 a = x2 & b = 5 a = 2x & b = y3 The formulas are: Sum of Two Cubes: a3 + b3 = (a + b) (a2 – ab + b2) Difference of Two Cubes: a3 – b3 = (a – b) (a2 + ab + b2) FIRST, determine what “a” and “b” are. Ex: 3. x6 – 125 Try: 4. 8x3 – y9 a = x2 & b = 5 a = 2x & b = y3 (a – b) (a2 + ab + b2) (a – b) (a2 + ab + b2) (x2 – 5) (x4 + 5x2 + 25) (2x – y3) (4x2 + 2xy3 + y6)

Factor Sum or Difference of 2 Cube worksheet Odds. Remember, the formulas are: Sum of Two Cubes: a3 + b3 = (a + b) (a2 – ab + b2) Difference of Two Cubes: a3 – b3 = (a – b) (a2 + ab + b2) Determine what “a” & “b” are. 5. 125x9 – y15 a = 5x3 & b = y5 (5x3 – y5) (25x6 + 5x3y5 + y10) 6. 16x12 + 54y18 2(8x12 + 27y18) a = 2x4 & b = 3y6 2 (2x4 + 3y6) (4x8 – 6x4y3 + 9y12) Factor Sum or Difference of 2 Cube worksheet Odds.