1. Bell Work Combine Like Terms 3 + 7 + 1 3x + 4x 4x + 3y + 2x + 6y
2xy + 12xy + 4yx

2. Defining Polynomials Adding Like Terms

3. Vocabulary 4x + 6x2 20xy – 4 3a2 - 5a + 4 - 4x 20x2yw3 -1/3 a2b3 3yz
Monomials
- 4x x2yw / a2b yz
Polynomials
4x + 6x xy – a2 - 5a + 4

4. Like Terms Which terms are like? 2x, -3, 5b, 0 -3 and 0
Which terms are like? x, 2x2, 4, x
3x and x
Which terms are like? wx, w, 3x, 4xw
2wx and 4xw

5. Adding Polynomials Add: (x2 + 3x + 1) + (4x2 +5)
Step 1: Underline like terms:
(x2 + 3x + 1) + (4x2 +5)
Step 2: Add the coefficients of like terms, do not change the powers of the variables:
(x2 + 4x2) + 3x + (1 + 5)
5x2 + 3x + 6

6. HERE IS THE STACK METHOD
Adding Polynomials
HERE IS THE STACK METHOD
(x2 + 3x + 1)
+ (4x )
(x2 + 3x + 1) + (4x2 +5)
5x2 + 3x + 6
Stack and add these polynomials:
(2a2 + 3ab + 4b2)
+ (7a2 + ab + -2b2)
(2a2+3ab+4b2) + (7a2+ab+-2b2)
9a2 + 4ab + 2b2

7. Find the sum or difference. (5a – 3b) + (2a + 6b)

8. Add the polynomials. + x2 + 3x + 7y + xy + 8 x2 + 4y + 2x + 31 1 Y 1 1 1 Y 1 1 1 Y
x2 + 3x + 7y + xy + 8
x2 + 4y + 2x + 3
3x + 7y + 8
x2 + 11xy + 8

9. Simplify: 3x2 – 4x + 8 x2 + x + 1 + 2x2 – 7x – 5 + 2x2 + 3x + 2
9.1 Adding and Subtracting Polynomials
Simplify:
3x2 – 4x + 8
x2 + x + 1
+ 2x2 – 7x – 5
+ 2x2 + 3x + 2
5x2 – 11x + 3
3x2 + 4x + 3
(4b b + 1)
+ (7b2 + b – 3)
a a – 5
+ 3a2 + 2a – 7
11b b – 2
4a a – 12

10. Simplify by finding the perimeter:
9.1 Adding and Subtracting Polynomials
Simplify by finding the perimeter:
x2 + x
c2 + 1
6c + 3 A B
2x2
2x2
4c2 + 2c + 5
x2 + x
A = 5c2 + 8c + 9
B = 6x2 + 2x

11. Subtracting Polynomials
(3x2 + 2x + 7) - (x2 + x + 4)
(3x2 + 2x + 7) + (- x2 + - x + - 4)
(3x2 + 2x + 7)
+ (- x2 + - x + - 4)
2x x + 3

12. Find the sum or difference. (5a – 3b) – (2a + 6b)

13. Simplify 3x2 – 7x + 5 7a2 – 2a – (5a2 + 3a) – (x2 + 4x + 7) 2a2 – 5a
9.1 Adding and Subtracting Polynomials
Simplify
3x2 – 7x + 5
7a2 – 2a
– (5a2 + 3a)
– (x2 + 4x + 7)
2a2 – 5a
2x2 – 11x – 2
7x2 – x + 3
4x2 + 3x + 2
– (3x2 – x – 7)
– (2x2 – 3x – 7)
2x2 + 6x + 9 4x

14. Simplify: 2x2 + 5x 3x2 – 2x + 10 – (2x2 + 4x – 6) – (x2 – 3)
9.1 Adding and Subtracting Polynomials
Simplify:
2x2 + 5x
3x2 – 2x + 10
– (2x2 + 4x – 6)
– (x2 – 3)
x2 – 6x + 16
x2 + 5x + 3
4x2 – x + 6
3x2 – 5x + 3
– (3x2 – 4)
– (2x2 – x – 4)
x2 – 4x + 7
x2 – x + 10

15. Subtracting Polynomials
Subtract the following polynomials by changing to addition (Keep-Change-Change.), then add:

16. Simplify: 7d2 + 7d z2 + 5z + 4 + 2d2 + 3d + 2z2 - 5 9d2 + 10d
9.1 Adding and Subtracting Polynomials
Simplify:
7d2 + 7d
z2 + 5z + 4
+ 2d2 + 3d
+ 2z2 - 5
9d d
3z z – 1
(2x2 – 3x + 5)
+ (4x2 + 7x – 2)
(a a – 4)
+ (8a2 – 8a)
6x2 + 4x + 3
9a2 – 2a – 4

17. Simplify: 3d2 + 5d – 1 7p2 + 5 + (–4d2 – 5d + 2) + (–5p2 – 2p + 3)
9.1 Adding and Subtracting Polynomials
Simplify:
3d2 + 5d – 1
7p2 + 5
+ (–4d2 – 5d + 2)
+ (–5p2 – 2p + 3)
–d2 + 1
2p2 – 2p + 8
(3x2 + 5x)
+ (4 – 6x – 2x2)
(x3 + x2 + 7)
+ (2x2 + 3x – 8)
x2 – x + 4
x3 + 3x2 + 3x – 1

18. Simplify: 4p2 + 5p 2x3 + x2 – 4 + (-2p + p + 7) + 3x2 – 9x + 7
9.1 Adding and Subtracting Polynomials
Simplify:
4p2 + 5p
2x3 + x2 – 4
+ 3x2 – 9x + 7
+ (-2p + p + 7)
2x3 + 4x2 – 9x + 3
4p p + 7
5y2 – 3y + 8
+ 4y3 – 9
(8cd – 3d + 4c)
+ (-6 + 2cd – 4d)
4y3 + 5y2 – 3y – 1
4c – 7d + 10cd – 6

19. Simplify: (12y3 + y2 – 8y + 3) + (6y3 – 13y + 5)
9.1 Adding and Subtracting Polynomials
Simplify:
(12y3 + y2 – 8y + 3) + (6y3 – 13y + 5)
(7y3 + 2y2 – 5y + 9) + (y3 – y2 + y – 6)
(6x5 + 3x3 – 7x – 8) + (4x4 – 2x2 + 9)
= 18y3 + y2 – 21y + 8
= 8y3 + y2 – 4y + 3
= 6x5 + 4x4 + 3x3 – 2x2 – 7x + 1

20. Simplify: (4x5 + 3x3 – 3x – 5) – (– 2x3 + 3x2 + x + 5)
9.1 Adding and Subtracting Polynomials
Simplify:
(4x5 + 3x3 – 3x – 5) – (– 2x3 + 3x2 + x + 5)
= 4x5 + 5x3 – 3x2 – 4x – 10
(4d4 – 2d2 + 2d + 8) – (5d3 + 7d2 – 3d – 9)
= 4d4 – 5d3 – 9d2 + 5d + 17
(a2 + ab – 3b2) – (b2 + 4a2 – ab)
= –3a2 + 2ab – 4b2

21. Simplify by finding the perimeter:
9.1 Adding and Subtracting Polynomials
Simplify by finding the perimeter:
2d2 + d – 4
3x2 – 5 x D C
3d2 – 5d
x2 + 7
3d2 – 5d
d2 + 7
D = 9d2 – 9d + 3
C = 8x2 – 10x + 14

22. Simplify by finding the perimeter:
9.1 Adding and Subtracting Polynomials
Simplify by finding the perimeter:
3x2 – 5x
a3 + 2a
a + 1 E F
x2 + 3
2a3 + a + 3
E = 3a3 + 4a + 4
F = 8x2 – 10x + 6