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
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