CHAPTER 6 6-4 Adding and subtracting polynomials

CHAPTER 6 6-4 Adding and subtracting polynomials

Objectives Add and subtract polynomials.

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.

Example 1: Adding and Subtracting Monomials

Add or subtract. A. 12p3 + 11p2 + 8p3 Solution: 12p3 + 11p2 + 8p3 Identify like terms. 12p3 + 8p3 + 11p2 Rearrange terms so

that like terms are together. 20p3 + 11p2 Combine like terms

Example #1 B. 5x2 – 6 – 3x + 8 Solution 5x2 – 6 – 3x + 8 Identify like terms. 5x2 – 3x + 8 – 6 Rearrange terms so

that like terms are together.

5x2 – 3x + 2 Combine like terms.

Example#1 Add or subtract. C. t2 + 2s2 – 4t2 – s2 t2 + 2s2 – 4t2 – s2 Identify like terms. t2 – 4t2 + 2s2 – s2 Rearrange terms so

that like terms are together. –3t2 + s2 Combine like terms

Check it out!! Add or subtract. a. 2s2 + 3s2 + s Solution: 5s2 + s b. 4z4 – 8 + 16z4 + 2 Solution: 20z4 – 6 c. 2x8 + 7y8 – x8 – y8 Solution: x8 + 6y8

Adding polynomials Polynomials can be added in either

vertical or horizontal form. In vertical form, align the like terms and

add:

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

7x2 + 9x + 3

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

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

= 7x2 + 9x + 3

Example 2: Adding Polynomials

Add A. (4m2 + 5) + (m2 – m + 6) B. (10xy + x) + (–3xy + y) C.

Check It Out! Example 2

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

Solution: 12a3 + 15a2 – 16a

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

Example 3A: Subtracting Polynomials

Subtract (x3 + 4y) – (2x3) Solution: Rewrite subtraction as addition of the

opposite. x3 + 4y) + (–2x3) x3 + 4y) + (–2x3) (x3 – 2x3) + 4y Group like terms together. –x3 + 4y Combine like terms.

Identify like terms.

Example 3B: Subtracting Polynomials

(7m4 – 2m2) – (5m4 – 5m2 + 8) Solution: Rewrite subtraction as addition of the opposite. (7m4 – 2m2) + (–5m4 + 5m2 – 8) (7m4 – 2m2) + (–5m4 + 5m2 – 8)identify like

terms (7m4 – 5m4) + (–2m2 + 5m2) – 8 group like

terms 2m4 + 3m2 – 8

Check It Out! Example 3

Subtract. (2x2 – 3x2 + 1) – (x2 + x + 1) Solution: –2x2 – x

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 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.

Solution (3x2 + 7x – 5)

8x2 + 3x + 6+(5x2 – 4x + 11)

Student guided practice Do even problems 1-12 in your book

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Homework Do even problems 16-30 in your book

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Closure Today we learned about adding and

subtracting polynomials Next class we are going to learn about

multiplying and dividing polynomials