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

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

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

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

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

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Another way to look at naming… (Pick one from each column) First Name by Exponent Middle Name by Terms Last Name Linear (1 st degree)Mono (1) NOMIAL *They all have the same last name. Quadratic (2 nd degree)Bi (2) Cubic (3 rd degree)Tri (3) ______ degree (4 and up) Poly (4 and up)

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More Examples… PolynomialDegree Classified by degree Classified by number of terms 6 –2 x 3x + 1 –x x – 5 4x 3 – 8x 2 x 4 – 7x 3 – 5x constant linear fourth degree quadratic cubic monomial binomial polynomial trinomial binomial

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

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

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

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

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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 4. Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a)

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

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

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Find the sum or difference. (5a – 3b) + (2a + 6b) 1.3a – 9b 2.3a + 3b 3.7a + 3b 4.7a – 3b

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Find the sum or difference. (5a – 3b) – (2a + 6b) 1.3a – 9b 2.3a + 3b 3.7a + 3b 4.7a – 9b

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