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

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

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)

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)

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

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)

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 2 + 2 x – 5 2 quadratic trinomial 4x 3 – 8x 3 cubic binomial 2 x 4 – 7x 3 – 5x + 1 4 fourth degree polynomial

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

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

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

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

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

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

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

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

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