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.

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

5x2 – 6 – 3x + 8

5x2 – 3x + 8 – 6

5x2 – 3x + 2

Identify like terms.Rearrange terms so that like

terms are together.Combine like terms.

Add or Subtract..

Adding and Subtracting Monomials

C. t2 + 2s2 – 4t2 – s2

t2 – 4t2 + 2s2 – s2

t2 + 2s2 – 4t2 – s2

–3t2 + s2

Identify like terms.Rearrange terms so that

like terms are together.Combine like terms.

D. 10m2n + 4m2n – 8m2n

10m2n + 4m2n – 8m2n

6m2n

Identify like terms.

Combine like terms.

Polynomials can be added and subtracted 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)

= 3x2 – x – 1

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

7x2 + 9x + 3

Example: Adding and Subtracting Polynomials

Example : Adding and Subtracting Polynomials

A. (4m2 + 5) + (m2 – m + 6)

4m2 + 5 + m2 – m + 6

4m2 + m2 –m +5 + 6

5m2 – m + 11

Polynomials can be added and subtracted by combining and adding as monomials.

B. (7m4 – 2m2) – (5m4 – 5m2 + 8)

Subtract.

Subtracting Polynomials

(x3 + 4y) – (2x3)

Subtract.

Subtracting Polynomials

(7m4 – 2m2) – (5m4 – 5m2 + 8)

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

(3x2 + 7x – 5)(5x2 – 4x + 11)

8x2 + 3x + 6

Plot A.Plot B.

Combine like terms.

+

Example 5

The profits of two different manufacturing plants can be modeled as shown, where x is the number of units produced at each plant.

Use the information above to write a polynomial that represents the total profits from both plants.

–0.03x2 + 25x – 1500 Eastern plant profit.

–0.02x2 + 21x – 1700 Southern plant profit.Combine like terms.

+–0.05x2 + 46x – 3200