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Mastering Polynomial Subtraction in Pre-Algebra: A Comprehensive Guide

In this Pre-Algebra lesson, students will learn how to subtract polynomials effectively. The goal is to understand the concept of finding the opposite of polynomials and employing subtraction through various methods, including horizontal and vertical formats. We will explore examples, practice problems, and clear step-by-step instructions to enhance understanding. By the end of this lesson, students will be able to successfully subtract polynomials and apply these skills to solve complex algebraic expressions.

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Mastering Polynomial Subtraction in Pre-Algebra: A Comprehensive Guide

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  1. Subtracting Polynomials 13-4 Pre-Algebra HOMEWORK Page 681 #25-29 Pre-Algebra

  2. Polynomials 13-1 Pre-Algebra Our Learning Goal Students will be able to classify, simplify, add and subtract polynomials.

  3. Polynomials 13-1 Pre-Algebra • Students will be able to classify, simplify, add and subtract polynomials by completing the following assignments. • Learn to classify polynomials by degree and by the number of terms. • Learn to simplify polynomials. • Learn to add polynomials. • Learn to subtract polynomials. • …..and that’s all folks!

  4. Subtracting Polynomials 13-4 Today’s Learning Goal Assignment Learn to subtract polynomials. Pre-Algebra

  5. Subtracting Polynomials 13-4 Warm Up Problem of the Day Lesson Presentation Pre-Algebra

  6. Subtracting Polynomials 13-4 Warm Up Write the opposite of each integer. 1.10 Subtract. 3. 19 – (–12) Add. 5. (3x2 + 7) + (x2– 3x) 6. (2m2 – 3m) + (–5m2 + 2) –10 2. –7 7 31 4. –16 – 21 –37 4x2– 3x + 7 –3m2– 3m + 2 Pre-Algebra

  7. Subtracting Polynomials 13-4 Problem of the Day Tara has 4 pairs of shorts, 3 tops, and 2 pairs of sandals. If she wants to wear a completely different outfit than she wore yesterday, how many combinations does she have to choose from? 6 Pre-Algebra

  8. Subtracting Polynomials 13-4 Learn to subtract polynomials. Pre-Algebra

  9. Subtracting Polynomials 13-4 Subtraction is the opposite of addition. To subtract a polynomial, you need to find its opposite. Pre-Algebra

  10. Subtracting Polynomials 13-4 Additional Example 1A & 1B: Finding the Opposite of a Polynomial Find the opposite of each polynomial. A. 8x3y4z2 –(8x3y4z2) The opposite of a is –a. –8x3y4z2 B. –3x4 + 8x2 –(–3x4 + 8x2) Distribute the sign. 3x4– 8x2 Pre-Algebra

  11. Subtracting Polynomials 13-4 Insert Lesson Title Here Try This: Example 1A & 1B Find the opposite of each polynomial. A. 4d2e3f3 –(4d2e3f3) –4d2e3f3 The opposite of a is –a. B. –4a2 + 4a4 –(–4a2 + 4a4) Distribute the sign. 4a2– 4a4 Pre-Algebra

  12. Subtracting Polynomials 13-4 Additional Example 1C: Finding the Opposite of a Polynomial Find the opposite of the polynomial. A. 9a6b4 + a4b2– 1 –(9a6b4 + a4b2– 1) Distribute the sign. –9a6b4 –a4b2 + 1 Pre-Algebra

  13. Subtracting Polynomials 13-4 Insert Lesson Title Here Try This: Example 1C Find the opposite of the polynomial. A. 9a6b4 + a4b2– 1 –(9a6b4 + a4b2– 1) –9a6b4 –a4b2 + 1 Distribute the sign. Pre-Algebra

  14. Subtracting Polynomials 13-4 To subtract a polynomial, add its opposite. Pre-Algebra

  15. Subtracting Polynomials 13-4 Additional Example 2A: Subtracting Polynomials Horizontally Subtract. A. (5x2 + 2x– 3) – (3x2 + 8x– 4) Add the opposite. = (5x2 + 2x– 3) + (–3x2– 8x+ 4) Associative property. = 5x2 + 2x– 3 – 3x2– 8x + 4 = 2x2– 6x + 1 Combine like terms. Pre-Algebra

  16. Subtracting Polynomials 13-4 Insert Lesson Title Here Try This: Example 2A Subtract. A. (2y3 + 3y + 5) – (4y3 + 3y + 5) Add the opposite. = (2y3 + 3y + 5) + (–4y3– 3y – 5) Associative property. = 2y3 + 3y + 5 – 4y3– 3y– 5 = –2y3 Combine like terms. Pre-Algebra

  17. Subtracting Polynomials 13-4 Additional Example 2B: Subtracting Polynomials Horizontally Subtract. B. (b2 + 4b – 1) – (7b2–b– 1) Add the opposite. = (b2 + 4b – 1) + (–7b2+b+ 1) Associative property. = b2 + 4b – 1 –7b2 + b + 1 = –6b2 + 5b Combine like terms. Pre-Algebra

  18. Subtracting Polynomials 13-4 Insert Lesson Title Here Try This: Example 2B Subtract. B. (c3 + 2c2+ 3) – (4c3–c2– 1) = (c3 + 2c2+ 3) + (–4c3+c2+ 1) Add the opposite. = c3 + 2c2+ 3 – 4c3 + c2 + 1 Associative property. = –3c3 + 3c2 + 4 Combine like terms. Pre-Algebra

  19. Subtracting Polynomials 13-4 You can also subtract polynomials in a vertical format. Write the second polynomial below the first one, lining up the decimal points. Pre-Algebra

  20. Subtracting Polynomials 13-4 Additional Example 3A: Subtracting Polynomials Vertically Subtract. A. (2n2– 4n + 9) – (6n2– 7n + 5) (2n2– 4n + 9) 2n2– 4n + 9 – (6n2 – 7n + 5) +–6n2 + 7n –5 Add the opposite. –4n2 + 3n + 4 Pre-Algebra

  21. Subtracting Polynomials 13-4 Insert Lesson Title Here Try This: Example 3A Subtract. A. (4r3 + 4r + 6) – (6r3 + 3r + 3) (4r3 + 4r + 6) 4r3 + 4r + 6 Add the opposite. – (6r3 + 3r + 3) + –6r3– 3r –3 –2r3 + r + 3 Pre-Algebra

  22. Subtracting Polynomials 13-4 Additional Example 3B: Subtracting Polynomials Vertically Subtract. B. (10x2 + 2x –7) – (x2 + 5x + 1) (10x2 + 2x –7) 10x2 + 2x –7 Add the opposite. – (x2 + 5x + 1) + –x2– 5x– 1 9x2– 3x– 8 Pre-Algebra

  23. Subtracting Polynomials 13-4 Insert Lesson Title Here Try This: Example 3B Subtract. B. (13y2– 2x + 5) – (y2 + 5x– 9) (13y2– 2x + 5) 13y2– 2x + 5 – (y2 + 5x– 9) + –y2– 5x + 9 Add the opposite. 12x2– 7x + 14 Pre-Algebra

  24. Subtracting Polynomials 13-4 Additional Example 3C: Subtracting Polynomials Vertically Subtract. C. (6a4– 3a2–8) – (–2a4 + 7) (6a4– 3a2–8) 6a4– 3a2–8 – (–2a4 + 7) + 2a4– 7 Add the opposite. 8a4 – 3a2– 15 Pre-Algebra

  25. Subtracting Polynomials 13-4 Insert Lesson Title Here Try This: Example 3C Subtract. C. (5x2 + 2x + 5) – (–3x2– 7x) (5x2 + 2x + 5) 5x2 + 2x + 5 +3x2 + 7x – (–3x2– 7x) Add the opposite. 8x2 + 9x+ 5 Pre-Algebra

  26. Subtracting Polynomials 13-4 Additional Example 4: Business Application Suppose the cost in dollars of producing x bookcases is given by the polynomial 250 + 128x, and the revenue generated from sales is given by the polynomial 216x– 75. Find a polynomial expression for the profit from producing and selling x bookcases, and evaluate the expression for x = 95. 216x – 75 – (250 + 128x) revenue – cost Add the opposite. 216x – 75 + (–250 – 128x) Associative Property 216x – 75 – 250 – 128x Combine like terms. 88x – 325 Pre-Algebra

  27. Subtracting Polynomials 13-4 Additional Example 4 Continued The profit is given by the polynomial 88x– 325. For x = 95, 88(95) – 325 = 8360 – 325 = 8035 The profit is $8035. Pre-Algebra

  28. Subtracting Polynomials 13-4 Insert Lesson Title Here Try This: Example 4 Suppose the cost in dollars of producing x baseball bats is given by the polynomial 6 + 12x, and the revenue generated from sales is given by the polynomial 35x– 5. Find a polynomial expression for the profit from producing and selling x baseball bats, and evaluate the expression for x = 50. 35x – 5 – (6 + 12x) revenue – cost Add the opposite. 35x – 5 + (–6 – 12x) Associative Property 35x – 5 – 6 – 12x 23x – 11 Combine like terms. Pre-Algebra

  29. Subtracting Polynomials 13-4 Insert Lesson Title Here Try This: Example 4 Continued The profit is given by the polynomial 23x– 11. For x = 50, 23(50) – 11 = 1150 – 11 = 1139 The profit is $1139. Pre-Algebra

  30. Subtracting Polynomials 13-4 Insert Lesson Title Here Lesson Quiz Find the opposite of each polynomial. Subtract. 3. (3z2 – 7z + 6) – (2z2 + z– 12) 2.–3m3 + 2m2n 3m3– 2m2n 1. 3a2b2c3 –3a2b2c3 z2– 8z + 18 4.–18h3– (4h3 + h2– 12h + 2) 5. (3b2c + 5bc2– 8b2) – (4b2c + 2bc2–c2) –22h3–h2 + 12h– 2 –b2c + 3bc2– 8b2 + c2 Pre-Algebra

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