Holt Algebra 1

7-6 Adding and Subtracting PolynomialsAdding and Subtracting Polynomials

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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

10y

3p

not like terms

3x + 12

–2t – 6

–x2 + 4x + 6

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add and subtract polynomials.

Objective

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add or Subtract..

Example 1: Adding and Subtracting Monomials

A. 12p3 + 11p2 + 8p3

12p3 + 11p2 + 8p3

12p3 + 8p3 + 11p2

20p3 + 11p2

Identify like terms.Rearrange terms so that like

terms are together.Combine like terms.

B. 5x2 – 6 – 3x + 8

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add or Subtract..

Example 1: Adding and Subtracting Monomials

C. t2 + 2s2 – 4t2 – s2

D. 10m2n + 4m2n – 8m2n

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

E. 2s2 + 3s2 + s

Add or subtract.

F. 4z4 – 8 + 16z4 + 2

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

G. 2x8 + 7y8 – x8 – y8

Add or subtract.

H. 9b3c2 + 5b3c2 – 13b3c2

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Polynomials can be added in either vertical or horizontal form.

In vertical form, align the like terms and add:

In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms.

(5x2 + 4x + 1) + (2x2 + 5x + 2)

= (5x2 + 2x2 + 1) + (4x + 5x) + (1 + 2)

= 7x2 + 9x + 3

5x2 + 4x + 1+ 2x2 + 5x + 2

7x2 + 9x + 3

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add.

Example 2: Adding Polynomials

A. (4m2 + 5) + (m2 – m + 6)

(4m2 + 5) + (m2 – m + 6)

(4m2 + m2) + (–m) +(5 + 6)

5m2 – m + 11

Identify like terms.

Group like terms together.

Combine like terms.

B. (10xy + x) + (–3xy + y)

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add.

Example 2C: Adding Polynomials

(6x2 – 4y) + (3x2 + 3y – 8x2 – 2y)

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Add.

Example 2D: Adding Polynomials

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Check It Out! Example 2

Add (5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a).

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

To subtract polynomials, remember that subtracting is the same as adding the opposite. To find the opposite of a polynomial, you must write the opposite of each term in the polynomial:

–(2x3 – 3x + 7)= –2x3 + 3x – 7

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Subtract.

Example 3A: Subtracting Polynomials

(x3 + 4y) – (2x3)

(x3 + 4y) + (–2x3)

(x3 + 4y) + (–2x3)

(x3 – 2x3) + 4y

–x3 + 4y

Rewrite subtraction as addition of the opposite.

Identify like terms.

Group like terms together.

Combine like terms.

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Subtract.

Example 3B: Subtracting Polynomials

(7m4 – 2m2) – (5m4 – 5m2 + 8)

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Subtract.

Example 3C: Subtracting Polynomials

(–10x2 – 3x + 7) – (x2 – 9)

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Subtract.

Example 3D: Subtracting Polynomials

(9q2 – 3q) – (q2 – 5)

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

Check It Out! Example 3

Subtract.

(2x2 – 3x2 + 1) – (x2 + x + 1)

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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.

Example 4: Application

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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)

(–4r2 – 3s2)

11m2 + 3m

18pq – 2p

20d2 – 2d – 7

5. (2.5ab + 14b) – (–1.5ab + 4b) 4ab + 10b

Holt Algebra 1

7-6 Adding and Subtracting Polynomials

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