LESSON 8 2 ADDING AND SUBTRACTING POLYNOMIALS Remember

LESSON 8. 2 ADDING AND SUBTRACTING POLYNOMIALS

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

Adding Polynomials Horizontal Method Vertical Method

Add the polynomials.

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

Opposite of a Polynomial Simplify.

NOW YOU TRY…

Simplify.

Simplify.

Application 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 3 x 2 + 7 x – 5, and the area of plot B can be represented by 5 x 2 – 4 x + 11. Write a polynomial that represents the total area of both plots of land. (3 x 2 + 7 x – 5) + (5 x 2 – 4 x + 11) 8 x 2 + 3 x + 6 Plot A. Plot B. Combine like terms.

Write an expression that represents the area of the shaded region in terms of x. x+2 1) 2) 3 9 6 55 xx ++ 22 2 x + 5 3 x + 7

Write an expression that represents the area of the shaded region in terms of x. 1) 2) 5 8 7 33

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

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