Lesson 9.1: Adding and Subtracting Polynomials, Combining Like Terms
This lesson, designed by Skip Tyler of Varina High School, covers the definitions necessary for adding and subtracting polynomials, including terms like
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About Lesson 9.1: Adding and Subtracting Polynomials, Combining Like Terms
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Slide1Lesson 9-1Adding and Subtracting Polynomials. (Combining Like Terms) Designed by Skip Tyler, Varina High School
Slide2Definitions you’ll need:nomial – term mono – 1 bi – 2 tri – 3 degree – highest exponent you have 1 – linear 2 – quadratic 3 – cubic
Slide3Applying 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)
Slide4Applying 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)
Slide5Look at the table onpg. 457 in your book!
Slide6Another 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)
Slide7More Examples…Polynomial Degree Classified by degree Classified by number of terms 6 –2 x 3 x + 1 – x 2 + 2 x – 5 4 x 3 – 8 x 2 x 4 – 7 x 3 – 5 x + 1 0 1 1 4 2 3 constant linear linear fourth degree quadratic cubic monomial monomial binomial polynomial trinomial binomial
Slide8Let’s look at how to…• Add and Subtract Polynomials • Remember to combine like terms!!!
Slide91. Add the following polynomials:(9y - 7x + 15a) + (-3y + 8x - 8a) Group your like terms. 9y - 3y - 7x + 8x + 15a - 8a 6y + x + 7a
Slide10Combine 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 )
Slide11Line 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 )
Slide12Rewrite subtraction as adding theopposite. (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)
Slide13Rewrite subtraction as adding theopposite. (7a - 10b) + ( - 3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b 5. Subtract the following polynomials: (7a - 10b) - (3a + 4b)
Slide14Line up your like terms and add theopposite. 4x 2 - 2xy + 3y 2 + ( + 3x 2 + xy - 2y 2 ) -------------------------------------- 7x 2 - xy + y 2 6. Subtract the following polynomials using column form: (4x 2 - 2xy + 3y 2 ) - (-3x 2 - xy + 2y 2 )
Slide15Find the sum or difference.(5a – 3b) + (2a + 6b) 1. 3a – 9b 2. 3a + 3b 3. 7a + 3b 4. 7a – 3b
Slide16Find the sum or difference.(5a – 3b) – (2a + 6b) 1. 3a – 9b 2. 3a + 3b 3. 7a + 3b 4. 7a – 9b
