Adding
and
Subtracting
6-4
6-4 Adding and Subtracting Polynomials
Polynomials
Warm Up
Lesson Presentation
Lesson Quiz
Holt
McDougal
Algebra
Holt
Algebra
1 1Algebra 1
6-4 Adding and Subtracting Polynomials
Warm Up
Simplify each expression by combining like
terms.
1. 4x + 2x 6x
2. 3y + 7y 10y
3. 8p – 5p 3p
4. 5n + 6n2 not like terms
Simplify each expression.
5. 3(x + 4) 3x + 12
6. –2(t + 3) –2t – 6
7. –1(x2 – 4x – 6) –x2 + 4x + 6
Holt McDougal Algebra 1
6-4 Adding and Subtracting Polynomials
Objective
Add and subtract polynomials.
Holt Algebra 1
6-4 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
6-4 Adding and Subtracting Polynomials
Example 1: Adding and Subtracting Monomials
Add or subtract.
A. 12p3 + 11p2 + 8p3
12p3 + 11p2 + 8p3
12p3 + 8p3 + 11p2
20p3 + 11p2
B. 5x2 – 6 – 3x + 8
5x2 – 6 – 3x + 8
5x2 – 3x + 8 – 6
5x2 – 3x + 2
Holt Algebra 1
Identify like terms.
Rearrange terms so that like
terms are together.
Combine like terms.
Identify like terms.
Rearrange terms so that like
terms are together.
Combine like terms.
6-4 Adding and Subtracting Polynomials
Example 1: Adding and Subtracting Monomials
Add or subtract.
C. t2 + 2s2 – 4t2 – s2
t2 + 2s2 – 4t2 – s2
t2 – 4t2 + 2s2 – s2
–3t2 + s2
Identify like terms.
Rearrange terms so that
like terms are together.
Combine like terms.
D. 10m2n + 4m2n – 8m2n
10m2n + 4m2n – 8m2n
Identify like terms.
6m2n
Combine like terms.
Holt Algebra 1
6-4 Adding and Subtracting Polynomials
Remember!
Like terms are constants or terms with the same
variable(s) raised to the same power(s). To
review combining like terms, see lesson 1-7.
Holt Algebra 1
6-4 Adding and Subtracting Polynomials
Check It Out! Example 1
Add or subtract.
a. 2s2 + 3s2 + s
2s2 + 3s2 + s
5s2 + s
Identify like terms.
Combine like terms.
b. 4z4 – 8 + 16z4 + 2
4z4 – 8 + 16z4 + 2
4z4 + 16z4 – 8 + 2
20z4 – 6
Holt Algebra 1
Identify like terms.
Rearrange terms so that
like terms are together.
Combine like terms.
6-4 Adding and Subtracting Polynomials
Check It Out! Example 1
Add or subtract.
c. 2x8 + 7y8 – x8 – y8
2x8
7y8
x8
y8
+
–
–
2x8 – x8 + 7y8 – y8
x8 + 6y8
Identify like terms.
Rearrange terms so that
like terms are together.
Combine like terms.
d. 9b3c2 + 5b3c2 – 13b3c2
9b3c2 + 5b3c2 – 13b3c2
b3c2
Holt Algebra 1
Identify like terms.
Combine like terms.
6-4 Adding and Subtracting 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
Holt Algebra 1
6-4 Adding and Subtracting Polynomials
Example 2: Adding Polynomials
Add.
A. (4m2 + 5) + (m2 – m + 6)
(4m2 + 5) + (m2 – m + 6)
Identify like terms.
(4m2 + m2) + (–m) +(5 + 6)
Group like terms
together.
Combine like terms.
5m2 – m + 11
B. (10xy + x) + (–3xy + y)
(10xy + x) + (–3xy + y)
Identify like terms.
(10xy – 3xy) + x + y
Group like terms
together.
Combine like terms.
7xy + x + y
Holt Algebra 1
6-4 Adding and Subtracting Polynomials
Example 2C: Adding Polynomials
Add.
(6x2 – 4y) + (3x2 + 3y – 8x2 – 2y)
(6x2 – 4y) + (3x2 + 3y – 8x2 – 2y) Identify like terms.
(6x2 – 4y) + (–5x2 + y)
(6x2 –5x2) + (–4y + y)
x2 – 3y
Holt Algebra 1
Combine like terms in the
second polynomial.
Combine like terms.
Simplify.
6-4 Adding and Subtracting Polynomials
Example 2D: Adding Polynomials
Add.
Identify like terms.
Group like terms
together.
Combine like terms.
Holt Algebra 1
6-4 Adding and Subtracting Polynomials
Check It Out! Example 2
Add (5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a).
(5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a)
Identify like terms.
(5a3 + 7a3) + (3a2 + 12a2) + (–10a – 6a) Group like terms
together.
12a3 + 15a2 – 16a
Holt Algebra 1
Combine like terms
6-4 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
6-4 Adding and Subtracting Polynomials
Example 3A: Subtracting Polynomials
Subtract.
(x3 + 4y) – (2x3)
(x3 + 4y) + (–2x3)
Rewrite subtraction as addition
of the opposite.
Identify like terms.
(x3 – 2x3) + 4y
Group like terms together.
–x3 + 4y
Combine like terms.
(x3 + 4y) + (–2x3)
Holt Algebra 1
6-4 Adding and Subtracting Polynomials
Example 3B: Subtracting Polynomials
Subtract.
(7m4 – 2m2) – (5m4 – 5m2 + 8)
(7m4 – 2m2) + (–5m4 + 5m2 – 8) Rewrite subtraction as
addition of the opposite.
(7m4 – 2m2) + (–5m4 + 5m2 – 8) Identify like terms.
(7m4 – 5m4) + (–2m2 + 5m2) – 8 Group like terms together.
2m4 + 3m2 – 8
Holt Algebra 1
Combine like terms.
6-4 Adding and Subtracting Polynomials
Example 3C: Subtracting Polynomials
Subtract.
(–10x2 – 3x + 7) – (x2 – 9)
(–10x2 – 3x + 7) + (–x2 + 9)
(–10x2 – 3x + 7) + (–x2 + 9)
–10x2 – 3x + 7
–x2 + 0x + 9
–11x2 – 3x + 16
Holt Algebra 1
Rewrite subtraction as
addition of the opposite.
Identify like terms.
Use the vertical method.
Write 0x as a placeholder.
Combine like terms.
6-4 Adding and Subtracting Polynomials
Example 3D: Subtracting Polynomials
Subtract.
(9q2 – 3q) – (q2 – 5)
(9q2 – 3q) + (–q2 + 5)
(9q2 – 3q) + (–q2 + 5)
9q2 – 3q + 0
+ − q2 – 0q + 5
8q2 – 3q + 5
Holt Algebra 1
Rewrite subtraction as
addition of the opposite.
Identify like terms.
Use the vertical method.
Write 0 and 0q as
placeholders.
Combine like terms.
6-4 Adding and Subtracting Polynomials
Check It Out! Example 3
Subtract.
(2x2 – 3x2 + 1) – (x2 + x + 1)
(2x2 – 3x2 + 1) + (–x2 – x – 1)
Rewrite subtraction as
addition of the opposite.
(2x2 – 3x2 + 1) + (–x2 – x – 1)
Identify like terms.
–x2 + 0x + 1
+ –x2 – x – 1
–2x2 – x
Holt Algebra 1
Use the vertical method.
Write 0x as a placeholder.
Combine like terms.
6-4 Adding and Subtracting Polynomials
Example 4: 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.
(3x2 + 7x – 5)
+ (5x2 – 4x + 11)
8x2 + 3x + 6
Holt Algebra 1
Plot A.
Plot B.
Combine like terms.
6-4 Adding and Subtracting Polynomials
Check It Out! Example 4
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
+ –0.02x2 + 21x – 1700
–0.05x2 + 46x – 3200
Holt Algebra 1
Eastern plant profit.
Southern plant profit.
Combine like terms.
6-4 Adding and Subtracting Polynomials
Lesson Quiz: Part I
Add or subtract.
1. 7m2 + 3m + 4m2
11m2 + 3m
2. (r2 + s2) – (5r2 + 4s2)
(–4r2 – 3s2)
3. (10pq + 3p) + (2pq – 5p + 6pq) 18pq – 2p
4. (14d2 – 8) + (6d2 – 2d +1) 20d2 – 2d – 7
5. (2.5ab + 14b) – (–1.5ab + 4b)
Holt Algebra 1
4ab + 10b
6-4 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
Holt Algebra 1