1. Warm Up Simplify each expression by combining like terms. 1. 4x + 2x 2. 3y + 7y 3. 8p – 5p 4. 5n + 6n 2 Simplify each expression. 5. 3(x + 4) 6. –2(t + 3) 7. –1(x 2 – 4x – 6) 6x6x 10y 3p3p not like terms 3x + 12 –2t – 6 –x 2 + 4x + 6

3. Like terms are constants or terms with the same variable(s) raised to the same power(s). Remember!

4. Horizontal Method Vertical Method Adding Polynomials

5. Add the polynomials.

6. When you use the Associative and Commutative Properties to rearrange the terms, the sign in front of each term must stay with that term. Remember!

7. Opposite of a Polynomial Simplify.

8. Subtract: (3x 2 + 2x + 7) - (x 2 + x + 4) Step 1: Change subtraction to addition (Keep-Change-Change.). Step 2: Underline OR line up the like terms and add. (3x 2 + 2x + 7) + (- x 2 + - x + - 4) (3x 2 + 2x + 7) + (- x 2 + - x + - 4) 2x 2 + x + 3 Subtracting Polynomials

9. Subtract the following polynomials by changing to addition (Keep-Change-Change.), then add:

10. Mark has $50 and owes his friends some money. He owes Jim $12, owes Carol $6, and owes Steve $10. Write an expression that could be used to calculate the remainder.

11. NOW YOU TRY…

12. Simplify.

14. A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of plot A can be represented by 3x 2 + 7x – 5, and the area of plot B can be represented by 5x 2 – 4x + 11. Write a polynomial that represents the total area of both plots of land. Application (3x 2 + 7x – 5) (5x 2 – 4x + 11) 8x 2 + 3x + 6 Plot A. Plot B. Combine like terms. +

15. Write an expression that represents the area of the shaded region in terms of x. 1)2) 3 6 2x + 5 x + 2 9 3x + 7 x + 2 5 5

16. Write an expression that represents the area of the shaded region in terms of x. 1)2) 5 7 8 3 3

17. Lesson Quiz: Part I Add or subtract. 1. 7m 2 + 3m + 4m 2 2. (r 2 + s 2 ) – (5r 2 + 4s 2 ) 3. (10pq + 3p) + (2pq – 5p + 6pq) 4. (14d 2 – 8) + (6d 2 – 2d + 1) –4r 2 – 3s 2 11m 2 + 3m 18pq – 2p 20d 2 – 2d – 7 5. (2.5ab + 14b) – (–1.5ab + 4b)4ab + 10b

18. Lesson Quiz: Part II 6. A painter must add the areas of two walls to determine the amount of paint needed. The area of the first wall is modeled by 4x 2 + 12x + 9, and the area of the second wall is modeled by 36x 2 – 12x + 1. Write a polynomial that represents the total area of the two walls. 40x 2 + 10