7-2 Add and Subtract Polynomials
Name
Date
Add: 5x2 4x 2x2 6x
5x2 4x 2x2 6x
Identify like terms.
(5x2 2x2) (4x 6x)
3x2 (2x)
3x2 2x
Apply the Commutative and Associative
Properties to group like terms.
Combine like terms.
Apply the definition of subtraction.
Subtract: (11x2y2 7xy2 13y4) (17x2y2 9xy2 5y4)
(11x2y2 7xy2 13y4) (17x2y2 9xy2 5y4)
Add the opposite of the polynomial being
subtracted and identify like terms.
(11x2y2 17x2y2) (7xy2 9xy2) (13y4 5y4)
Apply the Commutative and Associative
Properties to group like terms.
6x2y2 2xy2 18y4
Combine like terms.
Add or subtract like terms to simplify each expression. Use algebra tiles to help. Check students’ work.
1. (9x2 15x) (12x2 8x)
2. (16y2 21y) (8y2 3y)
9x2 ⴙ (ⴚ12x2) ⴙ 15x ⴙ 8x
ⴚ3x2 ⴙ 23x
3. (5g 4h 9gh) (13h 8gh 6g)
[16y2 ⴙ (–8y2)] ⴙ [21y ⴙ (ⴚ3y)]; 8y2 ⴙ 18y
4. (12t 8u 12tu) (7t 6u 4tu)
Copyright © by William H. Sadlier, Inc. All rights reserved.
[5g ⴙ (ⴚ6g)] ⴙ (4h ⴙ 13h) ⴙ [9gh ⴙ (ⴚ8gh)]
ⴚg ⴙ gh ⴙ 17h
5. 21n 19mn 15m 18mn 16m 14n
[21n ⴙ (ⴚ14n)] ⴙ [19mn ⴙ (ⴚ18mn)] ⴙ (ⴚ15m ⴙ 16m)
7n ⴙ m ⴙ mn
7. 1.5x2 3.8x 4.2x2 6.7 3.4x 9.2
[1.5x2 ⴙ (ⴚ4.2x2)] ⴙ (3.8x ⴙ 3.4x) ⴙ [ⴚ6.7 ⴙ (ⴚ9.2)]
ⴚ2.7x2 ⴙ 7.2x ⴚ 15.9
(12t ⴙ 7t) ⴙ [8u ⴙ (–6u)] ⴙ [12tu ⴙ (–4tu)]
19t ⴙ 2u ⴙ 8tu
6. 32k 16kᐉ 31k 15kᐉ 19ᐉ 17ᐉ
[32k ⴙ (ⴚ31k)] ⴙ [16kᐉ ⴙ (ⴚ15kᐉ) ⴙ 19ᐉ ⴙ (ⴚ17ᐉ)]
k ⴙ kᐉ ⴙ 2ᐉ
1
1
( 14 x
2
Perform the indicated operations.
9. Subtract (2m4 3mn3 2n4) from the sum
of (6m4 2mn3 16n4) and (6mn3 18n4).
6m4 ⴙ (ⴚ2mn3 ⴙ 6mn3) ⴙ (16n4 ⴙ 18n4)
6m4 ⴙ 4mn3 ⴙ 34n4
[6m4 ⴚ (ⴚ2m4)] ⴙ [4mn3 ⴚ (ⴚ3mn3)] ⴙ [34n4 ⴚ (ⴚ2n4)]
8m4 ⴙ 7mn3 ⴙ 36n4
3
4
3
1
8. 2 x 4 x2 4 2 x 8 x2 8
3
4
3
1
1
ⴙ x2 ⴙ x ⴙ x ⴙ ⴚ ⴙ ⴚ
8
2
4
8
2
1
7
5 2
x ⴙ2 xⴚ
2
8
8
) (
) [
( )]
10. Subtract (8v5 7v3w3 8w6) from the sum
of (10v5 6v3w3 10w6) and (9v5 14v3w3).
(10v5 ⴙ 9v5) ⴙ (ⴚ6v3w3 ⴙ 14v3w3) ⴙ 10w6
19v5 ⴙ 8v3w3 ⴙ 10w6
[19v5 ⴚ (ⴚ8v5)] ⴙ [8v3w3 ⴚ (ⴚ7v3w3)] ⴙ [10w6 ⴚ (ⴚ8w6)]
27v5 ⴙ 15v3w3 ⴙ 18w6
Lesson 7-2, pages 178–181.
Chapter 7
171
For More Practice Go To:
Solve. Show your work.
11. The figure below is a rectangle. Write an
expression that represents its perimeter.
12. The figure below is a square. Write an
expression that represents its perimeter.
2x 5y
2x 3y
3x 2y
(2x ⴚ 5y) ⴙ (2x ⴚ 5y) ⴙ (3x ⴚ 2y) ⴙ (3x ⴚ 2y)
(4x ⴚ 10y) ⴙ (6x ⴚ 4y); 10x ⴚ 14y
(2x – 3y) ⴙ (2x – 3y) ⴙ (2x – 3y) ⴙ (2x – 3y)
10x ⴚ 14y
8x – 12y
13. The perimeter of the quadrilateral below is
12x 10. Find an expression that represents
the length of the unmarked side.
14. The figure below is a regular pentagon.
Write an expression that represents its
perimeter.
2x 7
3x 8y
x4
3x 5
6x ⴙ 12
15. The lengths of the bases of an isosceles trapezoid
are 7x 1 and 11x 8. If the perimeter of the
trapezoid is 26x 15, what is the length of each
leg of the isosceles trapezoid?
(3x ⴙ 8y) ⴙ (3x ⴙ 8y) ⴙ (3x ⴙ 8y) ⴙ (3x ⴙ 8y) ⴙ (3x ⴙ 8y)
(3x ⴙ 3x ⴙ 3x ⴙ 3x ⴙ 3x) ⴙ (8y ⴙ 8y ⴙ 8y ⴙ 8y ⴙ 8y)
15x ⴙ 40y
16. The length of a side of square A is 7 more
than the length of a side of square B. If the
perimeter of square A is 8x 32, what is the
perimeter of square B?
26x ⴙ 15 ⴚ [(7x ⴙ 1) ⴙ (11x ⴙ 8)];
26x ⴙ 15 ⴚ (18x ⴙ 9)
8x ⴙ 6; The legs are congruent, so each is 4x ⴙ 3.
The perimeter of square A is 4(7) ⴝ 28 greater than
the perimeter of square B; 8x ⴙ 32 ⴚ 28 ⴝ 8x ⴙ 4;
The perimeter of square B is 8x ⴙ 4.
17. Simplify: (12x3 12x2 9x 12) (4x3 2x2 3x 7)
172
A. 8x3 14x2 6x 5
C. 8x3 14x2 12x 5
B. 8x3 14x2 6x 19
D. 8x3 14x2 12x 19
Chapter 7
Copyright © by William H. Sadlier, Inc. All rights reserved.
(12x ⴙ 10) – [(x – 4) ⴙ (2x ⴙ 7) ⴙ (3x – 5)]
(12x ⴙ 10) – (6x –2); 6x ⴙ 12