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**(Combining Like Terms)**

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 – bi – tri – 3 degree – highest exponent you have 1 – linear – 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) 3x2 + 2x – 4 or 2x + y – 4 (three terms)

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**Applying the Definitions:**

Examples of: linear quadratic cubic 2x or 4y + 2 (highest power is 1) 3x2 + 2x – 4 (highest power is 2) 2g3 + 3g2 + 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 (1st degree) Mono (1) NOMIAL *They all have the same last name. Quadratic (2nd degree) Bi (2) Cubic (3rd degree) Tri (3) ______ degree (4 and up) Poly (4 and up)

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**Classified by number of terms**

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

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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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**2. Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2)**

Combine your like terms. 3a2 + 3ab + 4ab - b2 + 6b2 3a2 + 7ab + 5b2

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**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

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**Rewrite subtraction as adding the opposite.**

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

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**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

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**Line up your like terms and add the opposite.**

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

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**Find the sum or difference. (5a – 3b) + (2a + 6b)**

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**Find the sum or difference. (5a – 3b) – (2a + 6b)**

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