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Mastering Polynomials: Add and Subtract with Ease

Learn how to simplify polynomial expressions by combining like terms. Practice addition and subtraction of polynomials to gain a strong understanding. Master essential skills with examples and step-by-step guidance. Assess your knowledge with a quiz.

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Mastering Polynomials: Add and Subtract with Ease

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  1. Adding and Subtracting Polynomials 6-4 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

  2. Warm Up 01/06/17 Simplify each expression by combining like terms. 1.4x + 2x 2. 8p – 5p Simplify each expression. 3. 3(x + 4) 4. –1(x2 – 4x – 6)

  3. Essential Objective Add and subtract polynomials.

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

  5. Example: Adding and Subtracting Monomials A. 12p3 + 11p2 + 8p3 Identify like terms. 12p3 + 11p2 + 8p3 20p3 + 11p2 Combine like terms. B. 5x2 – 6 – 3x + 8 Identify like terms. 5x2– 6 – 3x+ 8 5x2 – 3x + 2 Combine like terms.

  6. I do…. C. t2 + 2s2– 4t2 –s2 Identify like terms. t2+ 2s2– 4t2 – s2 t2– 4t2+ 2s2 – s2 –3t2+ s2 D. 10m2n + 4m2n– 8m2n 10m2n + 4m2n– 8m2n Identify like terms. 6m2n

  7. Remember! Like terms are constants or terms with the same variable(s) raised to the same power(s).

  8. We d0.... Add or subtract. a. 2s2 + 3s2 + s 2s2 + 3s2 + s 5s2 + s b. 4z4– 8 + 16z4 + 2 4z4– 8+ 16z4+ 2 4z4+ 16z4– 8+ 2 20z4 – 6

  9. You do…. Add or subtract. c. 2x8 + 7y8–x8–y8 x8 + 6y8 d. 9b3c2 + 5b3c2– 13b3c2 b3c2

  10. 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) + (4x + 5x) + (1 + 2) = 7x2+ 9x+ 3

  11. Example: Adding Polynomials

  12. 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 signs of each term: Change the signs and proceed to addition! –(2x3 – 3x + 7)= –2x3 + 3x– 7

  13. Example: Subtracting Polynomials (x3 + 4y) – (2x3) Rewrite subtraction as addition of the opposite. (x3 + 4y) + (–2x3) (x3 + 4y) + (–2x3) (x3– 2x3) + 4y –x3 + 4y Combine like terms.

  14. –10x2 – 3x + 7 –x2 + 0x+ 9 We do…. (–10x2 – 3x + 7) – (x2 – 9) Subtract. (–10x2 – 3x + 7) + (–x2+9) (–10x2 – 3x + 7) + (–x2+ 9) –11x2 – 3x + 16

  15. 9q2 – 3q+ 0 +− q2– 0q + 5 You do…. Subtract. (9q2 – 3q) – (q2 – 5) (9q2 – 3q) + (–q2+ 5) (9q2 – 3q) + (–q2 + 5) 8q2 – 3q + 5

  16. 8x2 + 3x + 6 Example: 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.

  17. Lesson Quiz 01/06/17 Add or subtract. 1. 7m2 + 3m + 4m2 2. (r2 + s2) – (5r2 + 4s2) 3. (10pq + 3p) + (2pq – 5p + 6pq) 4. (14d2 – 8) + (6d2 – 2d +1) 5. (2.5ab + 14b) – (–1.5ab + 4b)

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