CHAPTER 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. 12p p 2 + 8p 3  Solution:  12p p 2 + 8p 3 Identify like terms.  12p 3 + 8p p 2 Rearrange terms so that like terms are together.  20 p p 2 Combine like terms

Example #1  B. 5x 2 – 6 – 3x + 8  Solution  5x 2 – 6 – 3x + 8 Identify like terms.  5x 2 – 3x + 8 – 6 Rearrange terms so that like terms are together.  5 x 2 – 3 x + 2 Combine like terms.

Example#1  Add or subtract.  C. t 2 + 2s 2 – 4t 2 – s 2  t 2 + 2s 2 – 4t 2 – s 2 Identify like terms.  t 2 – 4t 2 + 2s 2 – s 2 Rearrange terms so that like terms are together.  –3t 2 + s 2 Combine like terms

Check it out!!  Add or subtract.  a. 2s 2 + 3s 2 + s  Solution: 5s 2 + s  b. 4z 4 – z  Solution: 20z 4 – 6  c. 2x 8 + 7y 8 – x 8 – y 8  Solution: x 8 + 6y 8

Adding polynomials  Polynomials can be added in either vertical or horizontal form.  In vertical form, align the like terms and add: 5x 2 + 4x x 2 + 5x + 2 7x2 + 9x + 37x2 + 9x + 3

 In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms.  (5x 2 + 4x + 1) + (2x 2 + 5x + 2)  (5x 2 + 2x 2 ) + (4x + 5x) + (1 + 2) = 7x 2 + 9x + 3

Example 2: Adding Polynomials  Add  A. (4m 2 + 5) + (m 2 – m + 6)  B. (10xy + x) + (–3xy + y)  C.

Check It Out! Example 2  Add (5a 3 + 3a 2 – 6a + 12a 2 ) + (7a 3 – 10a).  Solution: 12a a 2 – 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: –(2x 3 – 3x + 7)= –2x 3 + 3x – 7

Example 3A: Subtracting Polynomials  Subtract (x 3 + 4y) – (2x 3 )  Solution:  Rewrite subtraction as addition of the opposite.  x 3 + 4y) + (–2x 3 )  (x 3 – 2x 3 ) + 4y Group like terms together.  –x 3 + 4y Combine like terms. Identify like terms.

Example 3B: Subtracting Polynomials  (7m 4 – 2m 2 ) – (5m 4 – 5m 2 + 8)  Solution:  Rewrite subtraction as addition of the opposite.  (7m 4 – 2m 2 ) + (–5m 4 + 5m 2 – 8)  (7m 4 – 2m 2 ) + (–5m 4 + 5m 2 – 8)identify like terms  (7m 4 – 5m 4 ) + (–2m 2 + 5m 2 ) – 8 group like terms  2m 4 + 3m 2 – 8

Check It Out! Example 3  Subtract.  (2x 2 – 3x 2 + 1) – (x 2 + x + 1)  Solution:  –2x 2 – 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 3x 2 + 7x – 5 and the area of plot B can be represented by 5x 2 – 4x Write a polynomial that represents the total area of both plots of land.

Solution  (3x 2 + 7x – 5)  8x 2 + 3x + 6 +(5x 2 – 4x + 11)

Student guided practice  Do even problems 1-12 in your book page 417

Homework  Do even problems in your book page 417

Closure  Today we learned about adding and subtracting polynomials  Next class we are going to learn about multiplying and dividing polynomials