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Mastering Polynomial Addition and Subtraction: A Comprehensive Guide

This lesson explores the essential techniques for adding and subtracting polynomials by combining like terms. You'll learn the definitions of monomials, binomials, and trinomials, along with the concepts of polynomial degrees including linear, quadratic, and cubic forms. Through numerous examples such as (9y - 7x + 15a) + (-3y + 8x - 8a) and (4x² - 2xy + 3y²) - (-3x² - xy + 2y²), students will practice organizing and simplifying polynomial expressions effectively.

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Mastering Polynomial Addition and Subtraction: A Comprehensive Guide

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  1. Lesson 9-1 Adding and Subtracting Polynomials. (Combining Like Terms) Designed by Skip Tyler, Varina High School

  2. Definitions you’ll need: nomial – term mono – 1 bi – 2 tri – 3 degree – highest exponent you have 1 – linear 2 – quadratic 3 – cubic

  3. Applying the Definitions: Examples of: monomials binomials trinomials 2x or 4y or 6 (just one term) 2x + 4 or y – 8 (two terms) 3x2 + 2x – 4 or 2x + y – 4 (three terms)

  4. Applying the Definitions: Examples of: linear quadratic cubic 2x - 1 or 4y + 2 (highest power is 1) 3x2 + 2x – 4 (highest power is 2) 2g3 + 3g2 + 2g – 4 (highest power is 3)

  5. Look at the table on pg. 457 in your book!

  6. Another way to look at naming…(Pick one from each column)

  7. More Examples… Classified by number of terms Classified by degree Polynomial Degree constant monomial 6 0 linear monomial –2x 1 linear binomial 1 3x + 1 quadratic trinomial –x2 + 2x – 5 2 cubic binomial 3 4x3 – 8x fourth degree polynomial 4 2x4 – 7x3 – 5x + 1

  8. Let’s look at how to… • Add and Subtract Polynomials • Remember to combine like terms!!!

  9. 1. Add the following polynomials:(9y - 7x + 15a) + (-3y + 8x - 8a) Group your like terms. 9y - 3y - 7x + 8x + 15a - 8a 6y + x + 7a

  10. 2. Add the following polynomials:(3a2 + 3ab - b2) + (4ab + 6b2) Combine your like terms. 3a2 + 3ab + 4ab - b2 + 6b2 3a2 + 7ab + 5b2

  11. 3. Add the following polynomials using column form:(4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2) Line up your like terms. 4x2 - 2xy + 3y2 + -3x2 - xy + 2y2 _________________________ x2 - 3xy + 5y2

  12. 4. Subtract the following polynomials:(9y - 7x + 15a) - (-3y + 8x - 8a) Rewrite subtraction as adding the opposite. (9y - 7x + 15a) + (+ 3y - 8x + 8a) Group the like terms. 9y + 3y - 7x - 8x + 15a + 8a 12y - 15x + 23a

  13. 5. Subtract the following polynomials:(7a - 10b) - (3a + 4b) Rewrite subtraction as adding the opposite. (7a - 10b) + (- 3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b

  14. 6. Subtract the following polynomials using column form:(4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2) Line up your like terms and add the opposite. 4x2 - 2xy + 3y2 + (+ 3x2+ xy - 2y2) -------------------------------------- 7x2 - xy + y2

  15. Find the sum or difference.(5a – 3b) + (2a + 6b) • 3a – 9b • 3a + 3b • 7a + 3b • 7a – 3b

  16. Find the sum or difference.(5a – 3b) – (2a + 6b) • 3a – 9b • 3a + 3b • 7a + 3b • 7a – 9b

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