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Adding and Subtracting Polynomials. 7-6. Warm Up. Lesson Presentation. Lesson Quiz. Holt Algebra 1. Objective. Add and subtract polynomials. Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.

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  1. Adding and Subtracting Polynomials 7-6 Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

  2. Objective Add and subtract polynomials.

  3. Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.

  4. Example 1: Adding and Subtracting Monomials Add or Subtract.. A. 12p3 + 11p2 + 8p3 Identify like terms. 12p3 + 11p2 + 8p3 Rearrange terms so that like terms are together. 12p3 + 8p3 + 11p2 20p3 + 11p2 Combine like terms. B. 5x2 – 6 – 3x + 8 Identify like terms. 5x2– 6 – 3x+ 8 Rearrange terms so that like terms are together. 5x2 – 3x+ 8 – 6 5x2 – 3x + 2 Combine like terms.

  5. Example 1: Adding and Subtracting Monomials Add or Subtract.. C. t2 + 2s2– 4t2 –s2 Identify like terms. t2+ 2s2– 4t2 – s2 Rearrange terms so that like terms are together. t2– 4t2+ 2s2 – s2 –3t2+ s2 Combine like terms. D. 10m2n + 4m2n– 8m2n 10m2n + 4m2n– 8m2n Identify like terms. 6m2n Combine like terms.

  6. 5x2+ 4x+1 + 2x2+ 5x+ 2 7x2+9x+3 Polynomials can be added in either vertical or horizontal form. In vertical form, align the like terms and add: In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms. (5x2 + 4x + 1) + (2x2 + 5x+ 2) = (5x2 + 2x2 + 1) + (4x + 5x) + (1 + 2) = 7x2+ 9x+ 3

  7. Example 2: Adding Polynomials Add. A. (4m2 + 5) + (m2 – m + 6) (4m2+ 5) + (m2– m + 6) Identify like terms. Group like terms together. (4m2+m2) + (–m)+(5 + 6) 5m2 – m + 11 Combine like terms. B. (10xy + x) + (–3xy + y) Identify like terms. (10xy + x) + (–3xy + y) Group like terms together. (10xy– 3xy) + x +y 7xy+ x +y Combine like terms.

  8. 6x2– 4y + –5x2+ y Example 2C: Adding Polynomials Add. (6x2 – 4y) + (3x2 + 3y – 8x2 – 2y) (6x2– 4y) + (3x2+ 3y –8x2– 2y) Identify like terms. Group like terms together within each polynomial. (6x2 + 3x2 – 8x2) + (3y – 4y – 2y) Use the vertical method. Combine like terms. x2– 3y Simplify.

  9. Example 2D: Adding Polynomials Add. Identify like terms. Group like terms together. Combine like terms.

  10. To subtract polynomials, remember that subtracting is the same as adding the opposite. To find the opposite of a polynomial, you must write the opposite of each term in the polynomial: –(2x3 – 3x + 7)= –2x3 + 3x– 7

  11. Example 3A: Subtracting Polynomials Subtract. (x3 + 4y) – (2x3) Rewrite subtraction as addition of the opposite. (x3 + 4y) + (–2x3) (x3 + 4y) + (–2x3) Identify like terms. (x3– 2x3) + 4y Group like terms together. –x3 + 4y Combine like terms.

  12. Example 3B: Subtracting Polynomials Subtract. (7m4 – 2m2) – (5m4 – 5m2 + 8) (7m4 – 2m2) + (–5m4+5m2– 8) Rewrite subtraction as addition of the opposite. (7m4– 2m2) + (–5m4+ 5m2 – 8) Identify like terms. Group like terms together. (7m4– 5m4) + (–2m2+ 5m2) – 8 2m4 + 3m2 – 8 Combine like terms.

  13. –10x2 – 3x + 7 –x2 + 0x+ 9 Example 3C: Subtracting Polynomials Subtract. (–10x2 – 3x + 7) – (x2 – 9) (–10x2 – 3x + 7) + (–x2+9) Rewrite subtraction as addition of the opposite. (–10x2 – 3x + 7) + (–x2+ 9) Identify like terms. Use the vertical method. Write 0x as a placeholder. –11x2 – 3x + 16 Combine like terms.

  14. 8x2 + 3x + 6 Example 4: Application A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of plot A can be represented by 3x2 + 7x – 5 and the area of plot B can be represented by 5x2 – 4x + 11. Write a polynomial that represents the total area of both plots of land. (3x2 + 7x – 5) Plot A. (5x2– 4x + 11) Plot B. + Combine like terms.

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