Distributive property ppt
- 1. CHAPTER 2.5 The Distributive Property & Combining Like Terms
- 2. Vocabulary: terms: parts of an expression that are added together coefficient: number part of a term with a variable part like terms: have identical variable parts constant term: a term that has no variable
- 3. Example 3 Identify parts of an expression Identify the terms, like terms, coefficients, and constant terms of the expression 3x 4 6x 2.– – + SOLUTION Write the expression as a sum: 6x–( )4)3x –(+ + + 2 Terms: 6x,–3x, 4,– 2 Like terms: 3x and 6x;– 4 and 2– Coefficients: 3, 6– Constant terms: 4,– 2
- 4. The Distributive Property A (B + C) = AB + AC -A (B + C) = -AB - AC The distributive property says that a number next to the parentheses can be multiplied by each number inside the parentheses.
- 5. Example 5(3) + 5(4) = 15 + 20 = 35 5 (3 + 4) = 4(-1) + 4(3) = -4 + 12 = 8 4 (-1+ 3) =
- 6. Example 3(5) + 3(6) = 15 + 18 = 33 3 (5 + 6) = 2(-1) + 2(5) = -2 + 10 = 8 2 (-1 + 5) =
- 7. 3 (x + 2) x 1 1 x 1 1 x 1 1 3(x) + 3(2)= 3x + 6= Example
- 8. 2 (x2 + 2x - 2) 2(x2 ) + 2(2x)= 2x2 + 4x= Example 2(2)- x2 x2 x x x x -1 -1 -1 -1 - 4
- 9. Two practice problems 1. = 3 (2x2 ) – 3(10x) + 3(7) 2. = 6x2 – 30x + 21 1. = m (6x2 ) + m(4x) – m(12) 2. = 6x2 m + 4xm – 12m 3 (2x2 – 10x + 7) = m (6x2 + 4x – 12) =
- 10. Notes When multiplying by a negative number, use the distributive property and follow the rules for multiplying integers + • + = + or - • - = + (same signs = positive) - • + = - or + • - = - (opposite signs = negative)
- 11. Example -3(2x) + -3(4) = -6x + -12 -3 (2x + 4)= -2(-1x) ̶ -2(7) = 2x ̶ -14 = 2x + 14 -2 (-x – 7) =
- 12. Example -(-4x) + -(2) = 4x + -2 - (-4x + 2) = -12(x) ̶ -12(4) = -12x ̶ -48 = -12x + 48 -12 (x – 4)=
- 13. DISTRIBUTIVE PROPERTY Whiteboard Races!!! 1. We are in teams of 3 or 4. 2. Mr. Becker will give us a problem and EVERYONE will work it out silently on their boards for 30 seconds. 3. When Mr Becker says “team time”, we have an additional minute to compare our problems with our teammates 4. We will only get a point if everyone has the answer correct . 5. When Mr Becker says boards up, all boards go up. Any team who does not have all boards up with correct answers cannot score a point.
- 14. Problem 1 2 (x + 3)
- 15. 2 (x + 3) 2x + 6
- 16. Problem 2 3 (4 + 5x)
- 17. 3 (4 + 5x) 12 + 15x
- 18. Problem 3 -4(2x – 7)
- 19. -4(2x – 7) -8x + 28
- 20. Problem 4 -2(8 + 4x)
- 21. -2(8 + 4x) -16x – 8
- 22. Problem 5 - (3x – 5)
- 23. - (3x – 5) -3x + 5
- 24. Problem 6 - (8 + 12x)
- 25. - (8 + 12x) -8 – 12x
- 26. Problem 7 9 + 5(4x + 4)
- 27. 9 + 5(4x + 4) 20x + 29
- 28. Problem 8 2x + 3(5 + 4x)
- 29. 2x + 3(5 + 4x) 15 + 14x
- 30. Problem 9 2x + 3 – (x + 5)
- 31. 2x + 3 – (x + 5) x – 2
- 32. Problem 10 3x – (2x + 5) + 8
- 33. 3x – (2x + 5) + 8 x + 3
- 34. Problem 11 4x – 2(3x – 3)
- 35. 4x – 2(3x – 3) -2x + 6
- 36. Problem 12 7x + 3 – (6x + 5)
- 37. 7x + 3 – (6x + 5) x – 2
- 38. Problem 13 a (2x + 3)
- 39. a (2x + 3) 2xa + 3a
- 40. NOW YOU’RE AT BAT. YOU ARE SITTING SILENTLY WHILE I HAND OUT THE WORKSHEET. THE END!