1. Objectives The student will be able to: 1. add and subtract polynomials.

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

3. 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 )

4. 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 )

5. When adding polynomials, you also combine like terms. (2x 2 +3x-4) + (4x 2 +4x+8)

6. Work these on your paper using both methods. 1. (3x 2 +3x+3) + (4x 2 -2x+1) 2. (y 2 -8y+10) + (3y 2 +8y+10) 3. (3a 3 +7a-1) + (3a 2 +3a-4)

7. Add each of the following, as indicated. 1) (3x – 8) + (4x 2 – 3x +3) = 4x 2 + 3x – 3x – 8 + 3 = 4x 2 – 5 (a 2 – 3) + (5a 2 – 6a + 7) = 3x – 8 + 4x 2 – 3x + 3 Example Adding and Subtracting Polynomials

8. Subtracting polynomials: use either vertical or horizontal format. ***Remember to change the signs of every term in the second polynomial when you remove the ( )! Vertical format: (8x 4 -3x 2 -11x-3) – (-13x 4 -3x 2 +2x-17) 8x 4 - 3x 2 - 11x - 3 13x 4 +3x 2 -2x+17 (combine after changing signs) 21x 4 -13x+14

9. 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)

10. 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)

11. Line up your like terms and add the opposite. 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 )

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

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

14. Horizontal format: (8x 4 -3x 2 -11x-3) – (-13x 4 -3x 2 +2x-17) Remove ( ) changing the signs in the second polynomial. You are adding the opposites! 8x 4 -3x 2 -11x-3 + 13x 4 +3x 2 -2x+17 ( now combine like terms ) 21x 4 -13x+14 Classify this by degree and terms. 4, trinomial