Comprehensive Explanation to Adding and Subtracting Polynomials

1. Math 7 – Adding and
Subtracting Polynomials
Ms. Andi Fullido
© Quipper
And Teacher Andi’s Brain

2. Let’s review:
•Addition Rules?
•LASS?
•USB?
•Subtraction Rules?
•Copy-change-change
•Follow addition rules

3. Degree of a monomial?

4. Degree of a polynomial

5. Polynomials: Monomial, Trinomial,
Binomial, or NOTA?
1. 5x4 – 3x2 + x-1
2. 3x2 – 5x + 2
3. 2√x – 5x2
4. 7x –
2
𝑥2
5. 5xy –
4
5
y2
6. 4𝑥
1
2 − 2𝑥

6. Polynomials: Monomial, Trinomial,
Binomial, or NOTA?
1. 5x4 – 3x2 + x-1 – NOTA
2. 3x2 – 5x + 2 – Polynomial – Trinomial
3. 2√x – 5x2 – NOTA
4. 7x –
2
𝑥2 - NOTA
5. 5xy –
4
5
y2 – Polynomial – Binomial
6. 4𝑥
1
2 − 2𝑥 - NOTA

7. Polynomials: Monomial, Trinomial,
Binomial, or NOTA?
1. 5x4 – 3x2 + x-1 – NOTA
2. 3x2 – 5x + 2 – Polynomial – Trinomial
3. 2√x – 5x2 – NOTA
4. 7x –
2
𝑥2 - NOTA
5. 5xy –
4
5
y2 – Polynomial – Binomial
6. 4𝑥
1
2 − 2𝑥 - NOTA

8. Polynomials: Monomial, Trinomial,
Binomial, or NOTA?
1. 5x4 – 3x2 + x-1 – NOTA
- The exponent -1 is not a “nn” integer2√x –
5x2 – NOTA
1. 7x –
2
𝑥2 - NOTA
2. 5xy –
4
5
y2 – Polynomial – Binomial
3. 4𝑥
1
2 − 2𝑥 - NOTA

9. Polynomials: Monomial, Trinomial,
Binomial, or NOTA?
1. 5x4 – 3x2 + x-1 – NOTA
2. 3x2 – 5x + 2 – Polynomial – Trinomial
3. 2√x – 5x2 – NOTA
- A variable inside the radicand means it has
a fraction as an exponent
1. 5xy –
4
5
y2 – Polynomial – Binomial

10. Polynomials: Monomial, Trinomial,
Binomial, or NOTA?
1. 5x4 – 3x2 + x-1 – NOTA
2. 3x2 – 5x + 2 – Polynomial – Trinomial
3. 2√x – 5x2 – NOTA
4. 7x –
2
𝑥2 - NOTA
- There is a variable in the denominator
1. 4𝑥
1
2 − 2𝑥 - NOTA

11. Polynomials: Monomial, Trinomial,
Binomial, or NOTA?
1. 5x4 – 3x2 + x-1 – NOTA
2. 3x2 – 5x + 2 – Polynomial – Trinomial
3. 2√x – 5x2 – NOTA
4. 7x –
2
𝑥2 - NOTA
5. 5xy –
4
5
y2 – Polynomial – Binomial
6. 4𝑥
1
2 − 2𝑥 – NOTA – the exponent is a fraction

12. So sorry!
• The bases are:

13. Prompt
•Addition and subtraction of polynomials
mainly involve addition and subtraction of
the coefficients of similar (like) terms. The
terms in a polynomial are similar if its
variables (and exponents) are the same.
Terms with similar variables but different
exponents are dissimilar (unlike).

14. Similar and Dissimilar
•4xy and 3xy

15. Similar and Dissimilar
•4xy and 3xy

16. Similar and Dissimilar
•4xy and 3xy
•7xy2 and 5x3

17. Similar and Dissimilar
•4xy and 3xy
•7xy2 and 5x3

18. Similar and Dissimilar
•4xy and 3xy
•7xy2 and 5x3
•2x2 and -4x

19. Similar and Dissimilar
•4xy and 3xy
•7xy2 and 5x3
•2x2 and -4x

20. Similar and Dissimilar
•4xy and 3xy
•7xy2 and 5x3
•2x2 and -4x
•-3x2 and 5x2

21. Similar and Dissimilar
•4xy and 3xy
•7xy2 and 5x3
•2x2 and -4x
•-3x2 and 5x2

22. Steps in adding or subtracting:
1. Group terms that are similar (like). How do we
know if it’s similar or like? Check if VARIABLE
and EXPONENT are the SAME.
2. Operate.
3. Arrange in descending order, according to
degree.
4. Box final answer :D

23. Gets?
1. Pagsama-samahin ang like terms. Paano
malalaman kung like? Tingnan kung PAREHO
ang EXPONENT at VARIABLE.
2. I-add o i-subtract, o i-add at i-subtract.
3. Ayusin ayon sa degree ng polynomial, mataas -
mababa
4. Kahunan ang final answer :D