# 1 4 cancellation

28. Aug 2011
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### 1 4 cancellation

• 2. Any mathematics expression is the addition or subtractions of one or more quantities. Cancellation (of Factors)
• 3. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Cancellation (of Factors)
• 4. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms Cancellation (of Factors)
• 5. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. Cancellation (of Factors)
• 6. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. b. x(y + z) is one term, Cancellation (of Factors)
• 7. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. b. x(y + z) is one term, but it's expanded form xy + xz has two terms, xy and xz. Cancellation (of Factors)
• 8. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. b. x(y + z) is one term, but it's expanded form xy + xz has two terms, xy and xz. A quantity that is multiplied to other quantities is called a factor. Cancellation (of Factors)
• 9. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. b. x(y + z) is one term, but it's expanded form xy + xz has two terms, xy and xz. A quantity that is multiplied to other quantities is called a factor. Example B. a. 3x2yz has many factors Cancellation (of Factors)
• 10. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. b. x(y + z) is one term, but it's expanded form xy + xz has two terms, xy and xz. A quantity that is multiplied to other quantities is called a factor. Example B. a. 3x2yz has many factors; 3, Cancellation (of Factors)
• 11. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. b. x(y + z) is one term, but it's expanded form xy + xz has two terms, xy and xz. A quantity that is multiplied to other quantities is called a factor. Example B. a. 3x2yz has many factors; 3, x, y, Cancellation (of Factors)
• 12. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. b. x(y + z) is one term, but it's expanded form xy + xz has two terms, xy and xz. A quantity that is multiplied to other quantities is called a factor. Example B. a. 3x2yz has many factors; 3, x, y, yz, x2, yx2, but it's one term. Cancellation (of Factors)
• 13. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. b. x(y + z) is one term, but it's expanded form xy + xz has two terms, xy and xz. A quantity that is multiplied to other quantities is called a factor. Example B. a. 3x2yz has many factors; 3, x, y, yz, x2, yx2, but it's one term. b. x(y + z) has two factors, x and (y + z). Cancellation (of Factors)
• 14. Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. b. x(y + z) is one term, but it's expanded form xy + xz has two terms, xy and xz. A quantity that is multiplied to other quantities is called a factor. P Q Given a fraction , common factor of P and Q may be canceled. Terms may not be canceled. Example B. a. 3x2yz has many factors; 3, x, y, yz, x2, yx2, but it's one term. b. x(y + z) has two factors, x and (y + z). Cancellation (of Factors)
• 15. Cancellation (of Factors) Any mathematics expression is the addition or subtractions of one or more quantities. These quantities are called terms. Example A. a. 3xy + 2x – yz has three terms; 3xy, 2x and yz. b. x(y + z) is one term, but it's expanded form xy + xz has two terms, xy and xz. A quantity that is multiplied to other quantities is called a factor. P Q Given a fraction , common factor of P and Q may be canceled. Terms may not be canceled. In other words, in order to simplify a fraction, the fraction must be in the factored form. Example B. a. 3x2yz has many factors; 3, x, y, yz, x2, yx2, but it's one term. b. x(y + z) has two factors, x and (y + z).
• 19. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 Example C. a. Cancellation (of Factors)
• 20. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 = 3 + 1 3 + 3 Example C. a. Cancellation (of Factors)
• 21. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 = 3 + 1 3 + 3 Example C. a. x2y xz = xxy xz b. Cancellation (of Factors)
• 22. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 = 3 + 1 3 + 3 Example C. a. x2y xz = xxy xz = xy z , b. Cancellation (of Factors)
• 23. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 = 3 + 1 3 + 3 Example C. a. x2y xz = xxy xz = xy z , x2 + y xz , no cancellation!b. Cancellation (of Factors)
• 24. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 = 3 + 1 3 + 3 Example C. a. x2y xz = xxy xz = xy z , x2 + y xz , no cancellation!b. (x + y)(2x – y) (2x +y) (x + y) c. Cancellation (of Factors)
• 25. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 = 3 + 1 3 + 3 Example C. a. x2y xz = xxy xz = xy z , x2 + y xz , no cancellation!b. (x + y)(2x – y) (2x +y) (x + y) = 2x – y 2x + y , c. Cancellation (of Factors)
• 26. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 = 3 + 1 3 + 3 Example C. a. x2y xz = xxy xz = xy z , x2 + y xz , no cancellation!b. (x + y)(2x – y) (2x +y) (x + y) = 2x – y 2x + y , (x + y) + (2x – y) (2x + y)+ (x + y) c. Cancellation (of Factors)
• 27. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 = 3 + 1 3 + 3 Example C. a. x2y xz = xxy xz = xy z , x2 + y xz , no cancellation!b. (x + y)(2x – y) (2x +y) (x + y) = 2x – y 2x + y , (x + y) + (2x – y) (2x + y) + (x + y) c. No cancellation! Cancellation (of Factors)
• 28. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 = 3 + 1 3 + 3 Example C. a. x2y xz = xxy xz = xy z , x2 + y xz , no cancellation!b. (x + y)(2x – y) (2x +y) (x + y) = 2x – y 2x + y , (x + y) + (2x – y) (2x + y) + (x + y) = 3x 3x + 2y c. No cancellation! Cancellation (of Factors)
• 29. 4 6 = 2*2 2*3 = 2 3 4 6 = 3 + 1 3 + 3 = 3 + 1 3 + 3 Example C. a. x2y xz = xxy xz = xy z , x2 + y xz , no cancellation!b. (x + y)(2x – y) (2x +y) (x + y) = 2x – y 2x + y , (x + y) + (2x – y) (2x + y) + (x + y) = 3x 3x + 2y c. No cancellation! Cancellation (of Factors) All of them are terms! The ( )’s don’t serve any operational purposes.
• 30. 3(5) 3 3 + 5 3 Ex. Determine if the each of the following expressions is in the factored form. If not, write it in the factored form then reduce the expression by cancellation, if possible. 1. 2. xy x x + y x3. 4. 5. 8.xy + y y x + yx xy – y6. 7. y – x x – y9. (x + y) (x – y) (y – x) (x + y) 10. (x + y) + (x – y) (y – x) (x + y)11. (x + y)z + (x + y)z (y – x)(x + y)12. x(x + 2) + 2(x + 2) x (x + 2) 13. x(x + 1) + 6(x + 2) x (x + 2) 14. (x – 3)(x – 3) – (x + 2)(x + 2) (x – 3) (x + 2) 15. 3(5) + 7 3 x2 + y2 xy Cancellation (of Factors)