Warm UpSimplify each expression by combining like terms.

1. 4x + 2x

2. 3y + 7y

3. 8p – 5p

4. 5n + 6n2

Simplify each expression.

5. 3(x + 4)

6. –2(t + 3)

7. –1(x2 – 4x – 6)

6x

10y3pnot like terms

3x + 12

–2t – 6

–x2 + 4x + 6

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

Remember!

LESSON 3AADDING

POLYNOMIALS

A.2 The student will perform operations on polynomials, includingb) adding, subtracting, multiplying, and

dividing polynomials

VirginiaStandards

3 2 3(4x x 5x 7) ( 8x 2x 1)+ - - + - - +

34x- 2 x+ 7x- 6-

Horizontal Method

Vertical Method3 24x x 5x 7+ - -38x 2x 1- - +34x- 2 x+ 7x- 6-

Adding Polynomials

4 2 3 22) (7y 9y 6) (3y 10y 8)+ - + - -

3 31) (6x 4x 3) (9x 6x 11)- + + + -Add the polynomials.

315x 2x+ 8-

47y 2 y-3 3y+ 14-2

23) 4x 5x 2 3x 4x 7

- +- -

27x 9x- 5-

3 2

34) 6m 2m m m 7m 10

- +- - +

22m- 6m- 10+35m

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 3x2 + 7x –5, and the area of plot B can be represented by 5x2 – 4x + 11. Write a polynomial that represents the total area of both plots of land.

Application

(3x2 + 7x – 5)(5x2 – 4x + 11)8x2 + 3x + 6

Plot A.Plot B.Combine like terms.

+

Lesson Quiz: Part I

Add or subtract.

1. 7m2 + 3m + 4m2

2. (r2 + s2) + (5r2 + 4s2)

3. (10pq + 3p) + (2pq – 5p + 6pq)

4. (14d2 – 8) + (6d2 – 2d + 1)

6r2 + 5s2

11m2 + 3m

18pq – 2p

20d2 – 2d – 7

5. (2.5ab + 14b) + (–1.5ab + 4b) ab + 8b

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 4x2 + 12x + 9, and the area of the second wall is modeled by 36x2 – 12x + 1. Write a polynomial that represents the total area of the two walls.40x2 + 10

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!

Opposite of a Polynomial

(a b c)- + + = a- b- c-Simplify.

31) (x 4x 9)- + -

5 32) (y 2y 7y)- - +

4 33) (t t 9t 2)- + - -

3 24) (5y 8y 9y 3)- - + -

3x- 4x- 9+

5y- 3 2y+ 7y-

4t- 3 t- 9t+ 2+

3 5y- 2 8y+ 9y- 3+