1. Adding and
Subtracting Polynomials
MATHEMATICS 7
Quarter 2 Week 4
MR. CARLO JUSTINO J. LUNA

2. LEARNING COMPETENCY
Adds and subtracts polynomials (M7ALIId-2)
LEARNING OBJECTIVES
At the end of the discussion, the learners will
be able to:
• Add polynomials
• Subtract polynomials
• Solve problems involving addition and
subtraction of polynomials

3. LAMIYLOPNO
An algebraic expression that represents a sum of
one or more terms containing whole number
exponents on the variables
VOCABULARY
POLYNOMIAL

4. MONOMIAL
A polynomial with one term
VOCABULARY

5. BINOMIAL
A polynomial with two terms
VOCABULARY

6. TRINOMIAL
A polynomial with three terms
VOCABULARY

7. MULTINOMIAL
A polynomial with four or more terms
VOCABULARY

8. REVIEW
How do we add integers?
How do we subtract integers?

9. DRILL Add or subtract the following integers.
1. 13 + 8
2. 15 + (−4)
3. (−20) + (−9)
4. 8 − (−3)
5. −12 − 4

10. Activity:
We
Group
as One!

11. Activity:
We
Group
as One!

12. Analysis:
1. What did we do in our activity?
2. How did we group the objects?
Activity:
We
Group
as One!

13. Just as you can perform
operations on numbers, you
can perform operations on
polynomials.

14. What are Like Terms?
Like terms are terms that have the exact same variable part,
they must have the same variables raised to the same powers.
SAME VARIABLES, SAME EXPONENTS
3𝑥 and −5𝑥
−8𝑦2
and 12𝑦2
−5𝑎2𝑏5 and 7𝑎2𝑏5

15. You can only combine terms
together if they are like
terms.
If they aren't like terms, you must keep them separate.

16. 2𝑥 + 3𝑦 + 4𝑥
Let 𝑥 be a circle, and y be a triangle.
2𝑥 + 3𝑦 + 4𝑥
= 6𝑥 + 3𝑦

17. ADDITION OF POLYNOMIALS
To add like terms together, you add the coefficients and keep
the variable part the same.
𝟒𝒙 + 𝟑𝒙 = 𝟕𝒙
Add the coefficients. The variable part stays
the same.

18. ADDITION OF POLYNOMIALS
• There are two (2) common methods by which we add
algebraic expressions.
• Let’s take the following example:
(7𝑥𝑦 + 5𝑦𝑧 − 3𝑥𝑧) + (4𝑦𝑧 + 9𝑥𝑧 − 4𝑦) + (−2𝑥𝑦 − 3𝑥𝑧 + 5𝑥)

19. In vertical form, align the like terms and add.
(7𝑥𝑦 + 5𝑦𝑧 − 3𝑥𝑧) + (4𝑦𝑧 + 9𝑥𝑧 − 4𝑦) + (−2𝑥𝑦 − 3𝑥𝑧 + 5𝑥)
7𝑥𝑦 + 5𝑦𝑧 − 3𝑥𝑧
+ 4𝑦𝑧 + 9𝑥𝑧 − 4𝑦
+ − 2𝑥𝑦 − 3𝑥𝑧 + 5𝑥
5𝑥𝑦 + 9𝑦𝑧 + 3𝑥𝑧 + 5𝑥 − 4𝑦
Method 1

20. In horizontal form, use the Associative and
Commutative Properties to regroup and
combine like terms.
(7𝑥𝑦 + 5𝑦𝑧 − 3𝑥𝑧) + (4𝑦𝑧 + 9𝑥𝑧 − 4𝑦)
+ (−2𝑥𝑦 − 3𝑥𝑧 + 5𝑥)
= 7𝑥𝑦 − 2𝑥𝑦 + 5𝑦𝑧 + 4𝑦𝑧 +
−3𝑥𝑧 + 9𝑥𝑧 − 3𝑥𝑧 + 5𝑥 − 4𝑦
= 5𝑥𝑦 + 9𝑦𝑧 + 3𝑥𝑧 + 5𝑥 − 4𝑦
Method 2

21. Example 1: Adding Polynomials
A. (4m2 + 5) + (m2 – m + 6)
(4m2 + 5) + (m2 – m + 6)
(4m2 + m2) + (–m) +(5 + 6)
5m2 – m + 11
Identify like terms.
Group like terms together.
Combine like terms.
B. (10xy + x) + (–3xy + y)
(10xy + x) + (–3xy + y)
(10xy – 3xy) + x + y
7xy + x + y
Identify like terms.
Group like terms together.
Combine like terms.

22. Example 2: Adding Polynomials
(6x2 – 4y) + (3x2 + 3y – 8x2 – 2y)
Identify like terms.
Combine like terms in the
second polynomial.
Combine like terms.
(6x2 – 4y) + (3x2 + 3y – 8x2 – 2y)
(6x2 – 4y) + (–5x2 + y)
(6x2 –5x2) + (–4y + y)
x2 – 3y Simplify.

23. SUBTRACTION OF 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

24. Example 1: Subtracting Polynomials
Subtract.
(x3 + 4y) – (2x3)
(x3 + 4y) + (–2x3)
(x3 + 4y) + (–2x3)
(x3 – 2x3) + 4y
–x3 + 4y
Rewrite subtraction as addition
of the opposite.
Identify like terms.
Group like terms together.
Combine like terms.

25. Example 2: Subtracting Polynomials
Subtract.
(7m4 – 2m2) – (5m4 – 5m2 + 8)
(7m4 – 2m2) + (–5m4 + 5m2 – 8)
(7m4 – 5m4) + (–2m2 + 5m2) – 8
(7m4 – 2m2) + (–5m4 + 5m2 – 8)
2m4 + 3m2 – 8
Rewrite subtraction as
addition of the opposite.
Identify like terms.
Group like terms
together.
Combine like terms.

26. Example 3: 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
Rewrite subtraction as
addition of the opposite.
Identify like terms.
Use the vertical method.
Write 0x as a placeholder.
Combine like terms.

27. REAL-LIFE MATHEMATICS
A farmer must add the areas of two plots of land to determine
the number 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
Plot A.
Plot B.
Combine like terms.
+

28. REAL-LIFE MATHEMATICS
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 to the right 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

29. SUMMARY
ADDITION OF POLYNOMIALS
To add like terms together, you add the
coefficients and keep the variable part the same.
SUBTRACTION OF POLYNOMIALS
To subtract polynomials, remember that
subtracting is the same as adding the opposite.

30. Adding and
Subtracting
Polynomials
MATHEMATICS 7
Quarter 2 Week 4
SIR CJ LUNA