The document provides objectives and examples for adding and subtracting polynomials. The objectives are to: 1) Add polynomials 2) Subtract polynomials 3) Solve problems involving adding and subtracting polynomials. Examples are provided to demonstrate representing quantities with tiles, adding polynomials by grouping like terms, and subtracting polynomials using the keep, change, change process.

2. OBJECTIVES:
At the end of the lesson the students must
be able to;
1.Add polynomials
2.Subtract polynomials; and
3.Solve problems involving adding
and subtracting polynomials.

4. 1. What is the sum of 3x2
+ 5x-
9
and -3x+4?
a) 8x - 13
b) 3x2
- 2x +5
c) 3x2
+ 2x- 5
d) -3x2
-3x

5. 2. Subtract2x+2 from 9x+1
b) 11x-3
c) 7x-1
d) 11x
a) 7x-2

7. Algebraic Expressions Like
Terms
Unlik
e
Term
s
x , 2x, 3x, 4x
2x2, 2y2
2x, 2y
4xy2, xy2
6b, 6b3
2x2y, 2xy2
Put a check whether the expressions are like terms or unlike
terms

8. Like Terms or Similar Terms are
algebraic expressions with the
same variables and exponent
regardless of numerical
coefficient

9. Familiarize yourself with the Tiles below:
Stands for
+1
Stands for -
1
Stands for
+x
Stands for -
x
Stands for +
x2
Stands for -
x2
Can you represent the following quantities
using the tiles above?
1. x – 2
2. 4x +1

10. x – 2
Is the same
as

11. 4x +1
Is the same
as:

12. ACTIVITY 2
Represent the following quantities using the tiles.
*3𝑥2
+ 𝑥 − 2
*−2𝑥2 − 𝑥

13. To add polynomials group like terms horizontally or write
them in column form, aligning like terms.
(3x2 – 4x + 8) + (2x – 7x2 – 5)
Method 1: horizontal
Group like terms.
(3x2 – 7x2) + (-4x + 2x) + (8 – 5)
add like terms.
-4x2 – 2x + 3

14. Method 2: Vertical
3x2 – 4x + 8
+ -7x2 + 2x -5
- 4x2 – 2x + 3
Notice that terms are in descending
order with like terms aligned.

15. 1. What is the sum of 3x2
+ 5x-
9
and -3x+4?
a) 8x - 13
b) 3x2
- 2x +5
c) 3x2
+ 2x- 5
d) -3x2
-3x

16. Activity 3
Add
*(4𝑦3
+ 9y − 11) + (2𝑦2
− 3𝑦)

17. Activity 3
Add
*( −𝟓𝒙𝟐
+ 𝟏𝟎𝒙
𝒚 + 𝟒𝒚𝟐
) + (𝟕𝒙𝟐
+ 𝟖 × 𝒚 − 𝟔𝒚𝟐
)

18. 2x2 – 15x + 25
3x2 + 12x – 18
-
2x2 – 15x + 25
-3x2 - 12x + 18
+
-x2 – 27x + 43
Ex. (2x2 – 15x + 25) – (3x2 + 12x –
18)
CHANGE
KEEP
CHANGE
In subtracting polynomials, always remember the KEEP,
CHANGE, CHANGE process, then proceed to addition rule.

19. 2. (30x3 – 50x2 + 20x – 80) – (17x3 + 26x + 19)
- 17x3 + 26x +
19
30x3 – 50x2 + 20x - 80 30x3 – 50x2 + 20x -
80 -17x3 - 26x -
19
+
13x3 –
50x2
- 6x -
99
.
In subtracting polynomials, always remember the KEEP,
CHANGE, CHANGE process, then proceed to addition rule

20. .
*Example
If you have (100𝑥3 − 5𝑥2 + 3) pesos in your wallet and spent 80𝑥3 − 2𝑥2 + 9
pesos in your school canteen, how much money lest in your pocket?
Solution:
(100𝑥3 − 5𝑥2 + 3)
-
80𝑥3
− 2𝑥2
+ 9
(100𝑥3 − 5𝑥2 + 3)
+
−80𝑥3 + 2𝑥2 − 9
𝟐𝟎𝒙𝟑 − 𝟑𝒙𝟐 − 𝟔

21. 2. Subtract2x+2 from 9x+1
b) 11x-3
c) 7x-1
d) 11x
a) 7x-2

22. Subtract
.
*(5x+4) – (7x+2)

23. Subtract
.
*What must be added to 5x-8 to get
a result of 10x + 11?

24. Subtract
.
*Mary saved 3𝑥2
+ 17𝑥 − 10 from her allowance.
How much did she have after buying a gift worth
10x+7 for her sister’s birthday?

26. Proceed to
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