ADDITION AND SUBTRACTION OF POLYNOMIALS FOR GRADE 7

2. 1. What is the sum of 3x2
+ 2x + 1 and 5x -2?
b) 3x2
+ 7x -1
c) 3x2
- 7x + 1
b) -3x2
-3x -1
a) 10x - 1

3. 2. Subtract 2x2
– 5x + 1 from 5x2
-2x -1
b) 3x2
- 10x -2
c) 3x2
+ 3x + 2
b) -3x2
+ 3x + 2
a) 3x2
- 7x

6. NEXT
QUESTION
PLEASE
END

8. Algebraic Expressions Like Terms Unlike
Terms
x , 2x, 3x, 4x
2x2, 2y2
2x, 2y
4xy2, xy2
6b, 6b3
2x2y, 2xy2
2xy, -2xy, 3xy, 4yx
Put a check whether the expressions are like terms or unlike terms

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

10. 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

11. x – 2
Is the same as

12. 4x +1
Is the same as:

13. Use the tiles to find the sum of the following
polynomials;
1. 5x + 3x
2. (3x - 4) - 6x
3. (2x2
– 5x + 2) + (3x2
+ 2x)

14. 5x + 3x

15. (3x - 4) - 6x

16. (3x - 4) - 6x = -3x -4
+
+
+
=
=
=
0
0
0
Recall that combining +x and –x will result to zero

17. (2x2
– 5x + 2) + (3x2
+ 2x)
plus

18. (2x2
– 5x + 2) + (3x2
+ 2x)
plus

19. (2x2
– 5x + 2) + (3x2
+ 2x) = 5x2
- 3x + 2
Note: Combining +x and –x will result to zero, such that:
+
+
=
=
0
0

20. 2x2
– 5x + 2
3x2
+ 2x
5x2
- 3x + 2
+
Arrange the expressions according the degree of polynomial from highest to lowest, then arrange like terms in the same
column and proceed to operation.
ADD (2x2 – 5x + 2) and (3x2 + 2x)
2x2
– 5x + 2
3x2 + 2x
+

21. ADD (2x2 – 5x + 2) and (3x2 + 2x)
or
2x2 + 3x2 – 5x + 2x + 2
(2+ 3)x2 +(-5 + 2)x + 2
(5)x2 +(-3)x + 2
5x2 -3x + 2
Combine like terms, then add the numerical coefficient

22. 1. Add 4a – 3b + 2c, 5a + 8b – 10c and -12a + c.
2. Add 13x4– 20x3 + 5x – 10 and -10x2– 8x4– 15x + 10
4a – 3b + 2c
5a + 8b – 10c
-12a + c
- 3a 5b+ - 7c
13x4– 20x3 + 5x – 10
– 8x4 -10x2 15x 10+ +
5x4
-20x3
-10x2 +20x

23. 2x2– 15x + 25
3x2+ 12x – 18
-
2x2– 15x + 25
-3x2 - 12x + 18
+
-x2
– 27x + 43
Ex. (2x2 – 15x + 25) – (3x2 + 12x – 18)
(2x2 – 15x + 25) – (3x2 + 12x – 18)
2x2 – 15x + 25 - 3x2 - 12x + 18 Remove the parenthesis
2x2 - 3x2 - 15x - 12x + 25 + 18 Combine like terms
(2 – 3)x2 + (- 15 – 12)x + (25 + 18)
-x2 -27x + 43
Add numerical coefficient
Final Answer

24. 2. (30x3 – 50x2 + 20x – 80) – (17x3 + 26x + 19)
30x3 – 50x2 + 20x - 80
- 17x3 + 26x + 19
30x3 – 50x2 + 20x - 80
-17x3 - 26x - 19
+
13x3
– 50x2 - 6x - 99
To subtract polynomials, change the sign of the subtrahend then proceed to the addition rule. Also,
remember what subtraction means. It is adding the negative of the quantity.
or
(30x3 – 50x2 + 20x – 80) – (17x3 + 26x + 19)
30x3 – 50x2 + 20x – 80 – 17x3 -26x -19)
30x3 – 17x3 + 50x2 + 20x -26x – 80 -19
(30-17)x3 + 50x2 + (20 -26)x – 99
13x3 + 50x2 -6x – 99

27. Author:
JESUS M. ABALOS
Teacher I
Munoz National High School
Roxas, Isabela