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Chapter 9 Section 2

Chapter 9 Section 2. Adding and Subtracting Polynomials. What You’ll Learn. You’ll learn to add and subtract polynomials. Why It’s Important. Framing Addition of polynomials can be used to find the size of a picture.

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Chapter 9 Section 2

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  1. Chapter 9 Section 2 Adding and Subtracting Polynomials

  2. What You’ll Learn You’ll learn to add and subtract polynomials.

  3. Why It’s Important Framing Addition of polynomials can be used to find the size of a picture

  4. You can add polynomials by grouping the like terms together and then finding their sum.

  5. Example One Find each sum. (4x – 3) + (2x + 5) Add in column form. 4x – 3 Align the like terms. (+) 2x + 5 6x + 2

  6. Example Two Find each sum. (x2 + 2x – 5) + (3x2- x + 4) Add in column form. (x2 + 2x – 5) Align the like terms. (+) (3x2 - x + 4) 4x2+ x - 1

  7. Example Three Find each sum. (2x2 + 5xy + 3y2) + (8x2- 7y2) Add in column form. (2x2 + 5xy + 3y2) Align the like terms. (+) (8x2 - 7y2) 10x2 + 5xy – 4y2

  8. Your Turn Find each sum. (3x + 9) + (5x + 3) 3x + 9 + 5x + 3 8x + 12

  9. Your Turn Find each sum. (-2x2 + x + 5) + (x2 – 3x + 2) -2x2 + x + 5 + x2 – 3x + 2 -x2 - 2x + 7

  10. Your Turn Find each sum. a2 – 2ab + 4b2 + 7a2 - 2b2 8a2 – 2ab + 2b2

  11. Your Turn Find each sum. (7m2 - 6) + (5m - 2) 7m2 - 6 + 5m - 2 7m2 + 5m -8

  12. Review Recall that you can subtract an integer by adding its additive inverse or opposite. 2 – 3 = 2 + (-3) 5 – (-4) = 5 + 4 The additive inverse of 3 is -3. The additive inverse of -4 is 4.

  13. Similarly, you can subtract a polynomial by adding its additive inverse. • To find the additive inverse of a polynomial, replace each term with its additive inverse.

  14. -(a + 2) = -a – 2 -(x2 + 3x – 1) = -x2 - 3x + 1 -(2x2 - 5xy + y2) = -2x2 + 5xy - y2

  15. Example 4 Find each difference. (6x + 5) – (3x + 1) Arrange like terms in column form. 6x + 5 6x + 5 (-) 3x + 1 Add the additive inverse. (+) -3x – 1 3x + 4

  16. Example Five Find each difference. (2y2 – 3y + 5) – (y2 + 2y + 8) 2y2 – 3y + 5 (-) y2 + 2y + 8Add the additive inverse. 2y2 – 3y + 5 (+) -y2 - 2y – 8 y2 – 5y - 3

  17. Example Six Find each difference. (3x2 + 5) – (-4x + 2x2 + 3) Record the terms so that the powers of x are in descending order. 3x2 + 5 (-) 2x2 - 4x + 3 Add the additive inverse. 3x2 + 5 (+) -2x2 + 4x - 3 x2 + 4x + 2

  18. Your Turn Find each difference. (3x – 2) – (5x – 4) -2x + 2

  19. Your Turn Find each difference. (10x2 + 8x – 6) – (3x2 + 2x – 9) 7x2 + 6x + 3

  20. Your Turn Find each difference. 6m2 + 7 (–) -2m2 + 2m – 3 8m2 - 2m + 10

  21. Your Turn Find each difference. (5x2 - 4x) – (2 – 3x) 5x2 - x - 2

  22. Example Seven Word Problem The measure of the perimeter of triangle ABC is 7x + 2y. Find the measure of the third side of the triangle. B 3x – 5y 2x + y A C

  23. Example Seven Word Problem Explore: You know the perimeter of the triangle and the measures of two sides. You need to find AC, the measure of the third side. B 3x – 5y 2x + y A C

  24. Example Seven Word Problem Plan: The perimeter of a triangle is the sum of the measures of the three sides. To find AC, subtract the two given measures from the perimeter. B 3x – 5y 2x + y A C

  25. Example Seven Word Problem BC Solve: AC = Perimeter – AB – BC AC = (7x + 2y) – (2x + y) – (3x – 5y) AB B Perimeter 3x – 5y 2x + y A C

  26. Example Seven Word Problem Solve: AC = Perimeter – AB – BC AC = (7x + 2y) – (2x + y) – (3x – 5y) (7x + 2y) + (-2x – y) + (-3x + 5y) 7x + 2y -2x – y (+) –3x + 5y 2x + 6y Additive Inverse The measure of the third side is 2x + 6y. B 2x + y 3x – 5y A C

  27. Video Examples • Adding and Subtracting Polynomials

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