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  • 1. Adding & Subtracting Polynomials Mo du le 9 - To p ic 1
  • 2. What is a Polynomial? View this Cool Math lesson introducing Polynomials. There is only the 1 page of notes.
  • 3. Describe Polynomials View this Cool Math lesson introducing terms describing Polynomials. There are 3 pages of notes. Be sure to complete the Your Turn problems in your notebook. Check your answers on the next slides.
  • 4. Your Turn on Page 3 Find the degree of 3x - x2 .
  • 5. Your Turn on Page 3 Find the degree of 3x - x2 . The degree is 2.
  • 6. Your Turn on Page 3 Find the degree of 3x - x2 . The degree is 2. Find the degree of a 4b - 7a 2b2 .
  • 7. Your Turn on Page 3 Find the degree of 3x - x2 . The degree is 2. Find the degree of a 4b - 7a 2b2 . The degree is 5.
  • 8. Your Turn on Page 3 Find the degree of 3x - x2 . The degree is 2. Find the degree of a 4b - 7a 2b2 . The degree is 5. Find the degree of 7x - 1.
  • 9. Your Turn on Page 3 Find the degree of 3x - x2 . The degree is 2. Find the degree of a 4b - 7a 2b2 . The degree is 5. Find the degree of 7x - 1. The degree is 1.
  • 10. Adding & Subtracting Polynomials View this Cool Math lesson to learn how to add and subtract polynomials. There are 5 pages of notes. Be sure to complete the Try It and Your Turn problems in your notebook. Check your answers on the next slides.
  • 11. Try It on Page 2 Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z )
  • 12. Try It on Page 2 Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z ) Remove parenthesis.
  • 13. Try It on Page 2 Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z ) Remove parenthesis. 3x − 4w + z + 6x + 2w + 5z
  • 14. Try It on Page 2 Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z ) Remove parenthesis. 3x − 4w + z + 6x + 2w + 5z Rearrange so like terms are together.
  • 15. Try It on Page 2 Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z ) Remove parenthesis. 3x − 4w + z + 6x + 2w + 5z Rearrange so like terms are together. ( 3x + 6x ) + ( −4w + 2w ) + (1z + 5z )
  • 16. Try It on Page 2 Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z ) Remove parenthesis. 3x − 4w + z + 6x + 2w + 5z Rearrange so like terms are together. ( 3x + 6x ) + ( −4w + 2w ) + (1z + 5z ) Combine like terms.
  • 17. Try It on Page 2 Simplify: ( 3x − 4w + z ) + ( 6x + 2w + 5z ) Remove parenthesis. 3x − 4w + z + 6x + 2w + 5z Rearrange so like terms are together. ( 3x + 6x ) + ( −4w + 2w ) + (1z + 5z ) Combine like terms. 9x − 2w + 6z
  • 18. Your Turn on Page 3 Simplify. ( 8x 2 ) ( ) − x + 3 + 2x + 6x + 1 2
  • 19. Your Turn on Page 3 Simplify. ( 8x 2 ) ( ) − x + 3 + 2x + 6x + 1 2 Remove parenthesis.
  • 20. Your Turn on Page 3 Simplify. ( 8x 2 ) ( ) − x + 3 + 2x + 6x + 1 2 Remove parenthesis. 8x − x + 3 + 2x + 6x + 1 2 2
  • 21. Your Turn on Page 3 Simplify. ( 8x 2 ) ( ) − x + 3 + 2x + 6x + 1 2 Remove parenthesis. 8x − x + 3 + 2x + 6x + 1 2 2 Rearrange so like terms are together.
  • 22. Your Turn on Page 3 Simplify. ( 8x 2 ) ( − x + 3 + 2x + 6x + 1 2 ) Remove parenthesis. 8x − x + 3 + 2x + 6x + 1 2 2 Rearrange so like terms are together. ( 8x 2 ) + 2x + ( −x + 6x ) + ( 3 + 1) 2
  • 23. Your Turn on Page 3 Simplify. ( 8x 2 ) ( − x + 3 + 2x + 6x + 1 2 ) Remove parenthesis. 8x − x + 3 + 2x + 6x + 1 2 2 Rearrange so like terms are together. ( 8x 2 ) + 2x + ( −x + 6x ) + ( 3 + 1) 2 Combine like terms.
  • 24. Your Turn on Page 3 Simplify. ( 8x 2 ) ( − x + 3 + 2x + 6x + 1 2 ) Remove parenthesis. 8x − x + 3 + 2x + 6x + 1 2 2 Rearrange so like terms are together. ( 8x 2 ) + 2x + ( −x + 6x ) + ( 3 + 1) 2 Combine like terms. 10x + 5x + 4 2
  • 25. Try It on Page 3 Simplify. ( 4a b − ab + 3b 2 2 ) ( − 1 + a b + 8ab − 6a + 5 2 2 )
  • 26. Try It on Page 3 Simplify. ( 4a b − ab + 3b 2 2 ) ( − 1 + a b + 8ab − 6a + 5 2 2 ) Remove parenthesis.
  • 27. Try It on Page 3 Simplify. ( 4a b − ab + 3b 2 2 ) ( − 1 + a b + 8ab − 6a + 5 2 2 ) Remove parenthesis. 4a b − ab + 3b − 1 + a b + 8ab − 6a + 5 2 2 2 2
  • 28. Try It on Page 3 Simplify. ( 4a b − ab + 3b 2 2 ) ( − 1 + a b + 8ab − 6a + 5 2 2 ) Remove parenthesis. 4a b − ab + 3b − 1 + a b + 8ab − 6a + 5 2 2 2 2 Rearrange so like terms are together.
  • 29. Try It on Page 3 Simplify. ( 4a b − ab + 3b 2 2 ) ( − 1 + a b + 8ab − 6a + 5 2 2 ) Remove parenthesis. 4a b − ab + 3b − 1 + a b + 8ab − 6a + 5 2 2 2 2 Rearrange so like terms are together. ( 4a b + a b ) + ( −ab + 8ab ) + 3b 2 2 2 − 6a + ( −1 + 5 ) 2
  • 30. Try It on Page 3 Simplify. ( 4a b − ab + 3b 2 2 ) ( − 1 + a b + 8ab − 6a + 5 2 2 ) Remove parenthesis. 4a b − ab + 3b − 1 + a b + 8ab − 6a + 5 2 2 2 2 Rearrange so like terms are together. ( 4a b + a b ) + ( −ab + 8ab ) + 3b 2 2 2 − 6a + ( −1 + 5 ) 2 Combine like terms.
  • 31. Try It on Page 3 Simplify. ( 4a b − ab + 3b 2 2 ) ( − 1 + a b + 8ab − 6a + 5 2 2 ) Remove parenthesis. 4a b − ab + 3b − 1 + a b + 8ab − 6a + 5 2 2 2 2 Rearrange so like terms are together. ( 4a b + a b ) + ( −ab + 8ab ) + 3b 2 2 2 − 6a + ( −1 + 5 ) 2 Combine like terms. 5a b + 7ab + 3b − 6a + 4 2 2 2
  • 32. Your Turn on Page 4 Simplify. ( 3x 2 ) ( − 4x + 8 − x + 7x − 5 2 )
  • 33. Your Turn on Page 4 Simplify. ( 3x 2 ) ( − 4x + 8 − x + 7x − 5 2 ) Remove parenthesis but distribute the negative.
  • 34. Your Turn on Page 4 Simplify. ( 3x 2 ) ( − 4x + 8 − x + 7x − 5 2 ) Remove parenthesis but distribute the negative. 3x − 4x + 8 − x − 7x + 5 2 2
  • 35. Your Turn on Page 4 Simplify. ( 3x 2 ) ( − 4x + 8 − x + 7x − 5 2 ) Remove parenthesis but distribute the negative. 3x − 4x + 8 − x − 7x + 5 2 2 Rearrange so like terms are together.
  • 36. Your Turn on Page 4 Simplify. ( 3x 2 ) ( − 4x + 8 − x + 7x − 5 2 ) Remove parenthesis but distribute the negative. 3x − 4x + 8 − x − 7x + 5 2 2 Rearrange so like terms are together. ( 3x 2 −x 2 ) + ( −4x − 7x ) + ( 8 + 5 )
  • 37. Your Turn on Page 4 Simplify. ( 3x 2 ) ( − 4x + 8 − x + 7x − 5 2 ) Remove parenthesis but distribute the negative. 3x − 4x + 8 − x − 7x + 5 2 2 Rearrange so like terms are together. ( 3x 2 −x 2 ) + ( −4x − 7x ) + ( 8 + 5 ) Combine like terms.
  • 38. Your Turn on Page 4 Simplify. ( 3x 2 ) ( − 4x + 8 − x + 7x − 5 2 ) Remove parenthesis but distribute the negative. 3x − 4x + 8 − x − 7x + 5 2 2 Rearrange so like terms are together. ( 3x 2 −x 2 ) + ( −4x − 7x ) + ( 8 + 5 ) Combine like terms. 2x − 11x + 13 2
  • 39. Your Turn on Page 5 Subtract 3x − 6xy + y from x − 4xy + 5y . 2 2 2 2
  • 40. Your Turn on Page 5 Subtract 3x − 6xy + y from x − 4xy + 5y . 2 2 2 2 Write as a subtraction.
  • 41. Your Turn on Page 5 Subtract 3x − 6xy + y from x − 4xy + 5y . 2 2 2 2 Write as a subtraction. (x 2 2 ) ( − 4xy + 5y − 3x − 6xy + y 2 2 )
  • 42. Your Turn on Page 5 Subtract 3x − 6xy + y from x − 4xy + 5y . 2 2 2 2 Write as a subtraction. (x 2 2 ) ( − 4xy + 5y − 3x − 6xy + y 2 2 ) Remove parenthesis but distribute the negative.
  • 43. Your Turn on Page 5 Subtract 3x − 6xy + y from x − 4xy + 5y . 2 2 2 2 Write as a subtraction. (x 2 2 ) ( − 4xy + 5y − 3x − 6xy + y 2 2 ) Remove parenthesis but distribute the negative. x − 4xy + 5y − 3x + 6xy − y 2 2 2 2
  • 44. Your Turn on Page 5 Subtract 3x − 6xy + y from x − 4xy + 5y . 2 2 2 2 Write as a subtraction. (x 2 2 ) ( − 4xy + 5y − 3x − 6xy + y 2 2 ) Remove parenthesis but distribute the negative. x − 4xy + 5y − 3x + 6xy − y 2 2 2 2 Rearrange so like terms are together.
  • 45. Your Turn on Page 5 Subtract 3x − 6xy + y from x − 4xy + 5y . 2 2 2 2 Write as a subtraction. (x 2 2 ) ( − 4xy + 5y − 3x − 6xy + y 2 2 ) Remove parenthesis but distribute the negative. x − 4xy + 5y − 3x + 6xy − y 2 2 2 2 Rearrange so like terms are together. (x 2 2 ) − 3x + ( −4xy + 6xy ) + 5y − y( 2 2 )
  • 46. Your Turn on Page 5 Subtract 3x − 6xy + y from x − 4xy + 5y . 2 2 2 2 Write as a subtraction. (x 2 2 ) ( − 4xy + 5y − 3x − 6xy + y 2 2 ) Remove parenthesis but distribute the negative. x − 4xy + 5y − 3x + 6xy − y 2 2 2 2 Rearrange so like terms are together. (x 2 2 ) − 3x + ( −4xy + 6xy ) + 5y − y( 2 2 ) Combine like terms.
  • 47. Your Turn on Page 5 Subtract 3x − 6xy + y from x − 4xy + 5y . 2 2 2 2 Write as a subtraction. (x 2 2 ) ( − 4xy + 5y − 3x − 6xy + y 2 2 ) Remove parenthesis but distribute the negative. x − 4xy + 5y − 3x + 6xy − y 2 2 2 2 Rearrange so like terms are together. (x 2 2 ) − 3x + ( −4xy + 6xy ) + 5y − y ( 2 2 ) Combine like terms. −2x + 2xy + 4y 2 2
  • 48. Gizmo Practice Activity Let's practice some more at the Explore Learning website using the username and password given to you AND found in the support documents. Search for the "Addition of Polynomials - Activity A" Gizmo, launch the Gizmo and try at least 5 problems. After you have completed at least 5 Gizmo problems, scroll down to the Assessment Questions and complete the 4 multiple choice problems. Pronto or Message me if you have questions.
  • 49. Adding & Subtracting Polynomials Practice Practice Adding & Subtracting Polynomials at this Cool Math website. Select the “Give me a Problem” button to keep trying problems. Do your work in a notebook. When you select “What’s the Answer?” your answer is erased and correct answer is displayed. Having your work in a notebook will allow you to compare your answer to the correct answer. Keep working problems until you get 4 out of 5 correct.
  • 50. Way to Go! You’ve finished reviewing the notes for Adding and Subtracting Polynomials. Proceed to Module 9 Topic 1 Mastery Assignment.