```Name ________________________________________ Date __________________ Class __________________
LESSON
4-2
Reteach
You can add polynomials by combining like terms.
These are examples of like terms:
4y and 7y
8x2 and 2x2
m5 and 7m5
These are like terms because they have
the same variables and same exponent.
These are not like terms:
Add (5y2 + 7y + 2) + (4y2 + y + 8).
(5y2 + 7y + 2 ) + (4y2 + y + 8 )
2
2
(5y + 4y ) + ( 7y + y ) + ( 2 + 8 )
2
9y + 8y + 10
3x2 and 3x
4y and 7
same variable
but different
exponent
one with a
variable, one
is a constant
8m and 8n
different
variables
Identify like terms.
Rearrange terms so that like terms are together.
Combine like terms.
Add (5y2 + 7y + 2) + (4y2 + y + 8).
(5y2 + 7y + 2 ) + (4y2 + y + 8 )
Identify like terms.
(5y2 + 4y2) + ( 7y + y ) + ( 2 + 8 )
Rearrange terms so that like terms are together.
9y2 + 8y + 10
Combine like terms.
1. (6x2 + 3x) + (2x2 + 6x)
____________________________________________________
2. (m2 − 10m + 5) + (8m + 2)
____________________________________________________
3. (6x3 + 5x) + (4x3 + x2 − 2x + 9)
____________________________________________________
4. (2y5 − 6y3 + 1) + (y5 + 8y4 − 2y3 − 1) ____________________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
85
Name ________________________________________ Date __________________ Class __________________
LESSON
4-2
Practice and Problem Solving: Modified
Add. The first one is done for you.
1. 2m + 4
2.
3m + 6
________________________
12k + 3
+ 4k + 2
________________________
3.
+ 2y 2 + 2y + 9
+m+2
4.
3y 2 − y + 3
+ 2z 3 + z 2 − 3
_______________________
5.
6s 3 + 9s + 10
________________________
6.
+ 3s 3 + 4s − 10
15a 4+ 6a 2+a
+ 6a 4 − 2a 2 + a
_______________________
7. (3x3 + 4) + (x3 − 10)
4z 3 + 3z 2 + 8
________________________
8. (10g 2 + 3g − 10) + (2g 2 + g + 9)
________________________________________
________________________________________
9. (12p5 + 8) + (8p5 + 6)
10. (11b 2 + 3b − 1) + (2b 2 + 2b + 8)
________________________________________
________________________________________
Solve. The first one is started for you.
11. Rebecca is building a pen for her rabbits against the side of her house.
The polynomial 4n + 8 represents the length and the polynomial 2n + 6
represents the width.
a. What polynomial represents the perimeter
of the entire pen?
(4n
+ 8) + (4n + 8 ) + (2n + 6) + (2n + 6) =
_________________________________________
________________________________________
b. What polynomial represents the perimeter
of the pen NOT including the side of the house.
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
51
Name ________________________________________ Date __________________ Class __________________
LESSON
4-2
Practice and Problem Solving: A/B
Add the polynomial expressions using the vertical format.
1.
(10g 2 + 3g − 10)
2.
+ (2g 2 + g + 9)
________________________________________
3.
+ (3 x 3 + x 2 + 4 x )
________________________________________
(11b 2 + 3b − 1)
4.
+ (2b 2 + 2b + 8)
________________________________________
5.
(4 x 3 + x 2 + 2 x )
( c 3 + 2c 2 + 2c )
+ ( −3c 3 + c 2 − 4c )
________________________________________
(ab 2 + 13b − 4a )
6.
+ (3ab 2 + a + 7b )
________________________________________
( −r 2 + 8 pr − p )
+ ( −12r 2 − 2 pr + 8 p )
________________________________________
Add the polynomial expressions using the horizontal format.
7. (3y2 − y + 3) + (2y2 + 2y + 9)
8. (4z3 + 3z2 + 8) + (2z3 + z2 − 3)
________________________________________
________________________________________
9. (6s3 + 9s + 10) + (3s3 + 4s − 10)
10. (15a4 + 6a2 + a) + (6a4 − 2a2 + a)
________________________________________
________________________________________
11. (−7a2b3 + 3a3b − 9ab) + (4a2b3 − 5a3b + ab)
________________________________________
12. (2p4q2 + 5p3q − 2pq) + (8p4q2 − 3p3q − pq)
________________________________________
Solve.
13. A rectangular picture frame has the dimensions shown in
the figure. Write a polynomial that represents the perimeter
of the frame.
_________________________________________________________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
49
Int Math 2
Name___________________________________
Simplify each sum.
1) ( x 2 + 2) + (2 − 3x 3 − 8x 2 )
2) (8x 4 − 7x 3 ) + (2x 3 + 2x 2 − 2x 4 )
3) (2x 4 − 8) + (8x 4 + 7 + 2x)
4) (8k + 1) + (3k 2 + 3 − 2k)
5) (3 − 8n 4 ) + (3n 4 − 2n 3 + 6)
6) (4r 2 + 3r) + (8r + 4r 4 + 2r 2 )
7) (7n 3 + 7) + (6n 2 − 6 − 5n 3 )
8) (a 2 − 8) + (8a 2 + 5a 3 + 3)
9) (6x + x 2 ) + (7x − 1 − 5x 2 )
10) (2x 4 + 7x 2 ) + (3x 2 + 3x 4 − 5x)
Worksheet by Kuta Software LLC
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