The document contains practice problems for subtracting polynomials. It provides 14 problems where students are asked to find the opposite of given polynomials, subtract polynomials, and solve word problems involving subtracting polynomials to find quantities. The problems range in complexity from single term polynomials to multi-term polynomials.

1. MSM07G8_RESBK_Ch14_28-35.pe 2/15/06 10:48 AM Page 29
Name Date Class
LESSON Practice B
14-4 Subtracting Polynomials
Find the opposite of each polynomial.
1. 18xy 3 2. ؊9a ؉ 4 3. 6d 2 ؊ 2d ؊ 8
9a ؊ 4 9a ؊ 4 ؊6d 2 ؉ 2d ؉ 8
Subtract.
4. (4n 3 ؊ 4n ؉ 4n 2) ؊ (6n ؉ 3n 2 ؊ 8) 5. (؊2h 4 ؉ 3h ؊ 4) ؊ (2h ؊ 3h 4 ؉ 2)
4n 3 ؉ n 2 ؊ 10n ؉ 8 h4 ؉ h ؊ 6
6. (6m ؉ 2m 2 ؊ 7) ؊ (؊6m 2 ؊ m ؊ 7) 7. (17x 2 – x ؉ 3) – (14x 2 ؉ 3x ؉ 5)
8m 2 ؉ 7m 3x 2 ؊ 4x ؊ 2
8. w ؉ 7 ؊ (3w 4 ؉ 5w 3 ؊ 7w 2 ؉ 2w ؊ 10)
؊3w 4 ؊ 5w 3 ؉ 7w 2 ؊ w ؉ 17
9. (9r 3s ؊ 3rs ؉ 4rs 3 ؉ 5r 2s 2) ؊ (2rs 2 ؊ 2r 2s 2 ؉ 6rs ؉ 7r 3s ؊ 9)
2r 3s ؉ 7r 2s 2 ؉ 4rs 3 ؊ 2rs 2 ؊ 9rs ؉ 9
10. (3qr 2 ؊ 2 ؉ 14q 2r 2 ؊ 9qr) ؊ (؊10qr ؉ 11 ؊ 5qr 2 ؉ 6q 2r 2)
8؊ 13
11. The volume of a rectangular prism, in cubic meters, is given by
the expression x 3 ؉ 7x 2 ؉ 14x ؉ 8. The volume of a smaller
rectangular prism is given by the expression x 3 ؉ 5x 2 ؉ 6x.
How much greater is the volume of the larger rectangular prism?
2x 2 ؉ 8x ؉ 8 cubic meters
12. Sarah has a table with an area, in square inches, given by the
expression of y 2 ؉ 30y ؉ 200. She has a tablecloth with an area,
in square inches, given by the expression of y 2 ؉ 18y ؉ 80.
She wants the tablecloth to cover the top of the table. What
expression represents the number of square inches of additional
fabric she needs to cover the top of the table?
1are inches of fabric
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2. MSM07G8_RESBK_Ch14_52-64.pe 2/15/06 11:10 AM Page 58
LESSON Puzzles, Twisters & Teasers LESSON Practice A
14-3 It’s Amazing! 14-4 Subtracting Polynomials
Make your way through the maze by finding the sum of each Find the opposite of each polynomial.
set of polynomials. You may move up, down, left, right or
1. xy 2 2. ؊8p 4q 3 3. 5 ؊ 12a
diagonally, but you may not enter a square more than once.
Sum 2 4 3
؊xy 8p q 12a ؊ 5
1. (5x 2 ؊ 4x) ؉ (3x 2 ؉ 7x ؊ 2) 8x 2 ؉ 3x ؊ 2 4. 4k 3j ؉ 3k 5. 2u 2 ؊ 6u ؉ 9 6. ؊d 4e 3 ؊ 2d 3e 4 ؊ 8de
2. (؊6x 2 ؉ x ؊ 8) ؉ (11x 2 ؊ 5x) 5x 2 ؊ 4x ؊ 8
؊4k 3j ؊ 3k ؊2u 2 ؉ 6u ؊ 9 d 4e 3 ؉ 2d 3e 4 ؉ 8de
3. (2x 2 ؉ 12x ؊ 14) ؉ (؊8x 2 ؊ 15x) ؉ (7x ؉ 20) ؊6x 2 ؉ 4x ؉ 6
4. 10x 2 ؊ 4x ؉ 17 Subtract.
؉ 3x 2 ؉ 9x ؊ 20 13x 2 ؉ 5x ؊ 3 7. (b 2 ؉ 9) ؊ (3b 2 ؊ 5) 8. (2x 2 ؊ 3x) ؊ (x 2 ؉ 7)
3 2
5. 6x ؊ 3x ؉ 7x ؉ 4
11x 3 ؉ 8x 2 ؉ 7x ؊ 6 ؊2b 2 ؉ 14 x 2 ؊ 3x ؊ 7
؉ 5x 3 ؉ 11x 2 ؊ 10
2 2
9. (–2x ؉ 8x ؉ 9) ؊ (9x ؉ 6x ؊ 2) 10. (5y ؉ 8y 2 ؉ y) ؊ (9y 3 ؉ 7y 2 ؊ 2)
3
؊11x 2 ؉ 2x ؉ 11 ؊4y 3 ؉ y 2 ؉ y ؉ 2
8x 2 ؊ 3x 5x 2 ؉ 4x 2 ؉ 9 ؊ ؉ 11. (5q ؉ q ؉ q ؉ 2q ؊ 5q ؉ 3) ؊ (3 ؊ 2q ؉ q 2 ؊ 10q)
5 4 3 2 3
؉ 2x 2 17x 2 ؊ 6x ؉ 3x 2 5 ؉
5q 5 ؉ q 4 ؉ 3q 3 ؉ q 2 ؉ 5q
12. ؊2f ؊ (f 4 ؉ 3f 3g ؉ 2f 2g ؊ 3fg ؊ 2f ؊ 10)
7x 3x ؊؊ ؊ ؉ 12x 2 4x 13 ؉ 8x 6x
؊f 4 ؊ 3f 3g ؊ 2f 2g ؉ 3fg ؉ 10
؉ ؉ 4x 2 18 12 ؊ 6 11x 3 ؉ 11x 3
13. (nm 2 ؊ 2n 3 ؉ 4n 2m 2 ؊ nm ؉ 15) ؊ (؊10nm ؉ 4n 2 ؊ 5nm 2 ؉ 6n 2m 2 ؊ 2n 3)
13x 2 ؊ ؊6x؊؊ 8
2 9 3 ؊ 7 4x 2
؊2n 2m 2 ؉ 6nm 2 ؊ 4n 2 ؉ 9nm ؉ 15
؊5x 2 4x ؊ ؉
؊ 6x 13x 2 ؊ 5x ؊ 6x 2 ؊8x 2
14. Suppose the number of boxes (in millions) of crayons
manufactured annually by the Great Crayon Company is shown
8x 2 4x 2 ؉؊ 6
؊ ؉ 13 9x 6x 2 8x 2؊ ؉
؊ by the expression 9x 2 ؊ 8x ؉ 7. If the rest of the crayon-
making companies manufacture 6x 2 ؊ 3x ؉ 4 crayons, how
؊ ؊ 3 ؉ 5x 13x 14x ؉ 7x 2 7x many more crayons does The Great Crayon Company
manufacture each year than the rest of the crayon-making
companies?
؊2x 2 11x 2 ؉ ؉ ؊ 37 11x 3 ؊ 5x 2 ؊
3x 2 ؊ 5x ؉ 3 crayons
8 5x 8x 8x 2 ؉ 3 11x 2 14x 2 ؉ 6
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28 Holt Mathematics
LESSON Practice B LESSON Practice C
14-4 Subtracting Polynomials 14-4 Subtracting Polynomials
Find the opposite of each polynomial. Find the opposite of each polynomial.
1
1. 18xy 3 2. ؊9a ؉ 4 3. 6d 2 ؊ 2d ؊ 8 1. ᎏᎏc 5d 4e
8
2. ؊1.9f ؉ 4g ؊ 2.8h 4 3. mn 2 ؉ mn ؊ m 2n
1
؊18xy 3 9a ؊ 4 ؊6d 2 ؉ 2d ؉ 8 ؊ᎏᎏc 5d 4e
8 1.9f ؊ 4g ؉ 2.8h 4 ؊mn 2 ؊ mn ؉ m 2n
Subtract. Subtract.
4. (4n 3 ؊ 4n ؉ 4n 2) ؊ (6n ؉ 3n 2 ؊ 8) 5. (؊2h 4 ؉ 3h ؊ 4) ؊ (2h ؊ 3h 4 ؉ 2) ΂
1 3
4. k 3 ؊ ᎏᎏk ؉ ᎏᎏk 2 ؊ ᎏᎏk ؉ ᎏᎏk 2 ؊ 6
4 4 2 4 ͒ ͑1 3
͒
3
3
3
4n ؉ n ؊ 10n ؉ 8 2 4
h ؉h؊6 k ؉ ᎏᎏk ؉ 6
4
6. (6m ؉ 2m 2 ؊ 7) ؊ (؊6m 2 ؊ m ؊ 7) 7. (17x 2 – x ؉ 3) – (14x 2 ؉ 3x ؉ 5)
5. (100m 2 ؊ 25m 3 ؉ 35) ؊ (94m 2 ؉ 30m ؉ 5m 3 ؊ 25)
8m ؉ 7m2 2
3x ؊ 4x ؊ 2 ؊30m 3 ؉ 6m 2 ؊ 30m ؉ 60
4 3 2
8. w ؉ 7 ؊ (3w ؉ 5w ؊ 7w ؉ 2w ؊ 10) 6. (17n 3p ؊ 12np ؉ 4np 3 ؉ 19) ؊ (12np 3 ؉ 6np ؉ 7n 3p ؊ 9)
؊3w 4 ؊ 5w 3 ؉ 7w 2 ؊ w ؉ 17 10n 3p ؊ 8np 3 ؊ 18np ؉ 28
͑1 ͒
3 3 2 2 2 2 2 3
9. (9r s ؊ 3rs ؉ 4rs ؉ 5r s ) ؊ (2rs ؊ 2r s ؉ 6rs ؉ 7r s ؊ 9) 7. 13q 5r 5 ؊ ᎏᎏq3 ؉ 2r 6 ؊ 10 ؊ 11q 5r 5
25
2r 3s ؉ 7r 2s 2 ؉ 4rs 3 ؊ 2rs 2 ؊ 9rs ؉ 9 1
2q r ؊ ᎏᎏq 3 ؊ 2r 6 ؉ 10
5 5
25
10. (3qr 2 ؊ 2 ؉ 14q 2r 2 ؊ 9qr) ؊ (؊10qr ؉ 11 ؊ 5qr 2 ؉ 6q 2r 2)
8. (3st 2 ؊ 2s 3 ؉ 14s 2t 2) ؊ (؉ 4s 2 ؊ 5st 2 ؉ 6s 2t 2) ؊ (؊3s 3 ؉ 14s 2)
8q 2r 2 ؉ 8qr 2 ؉ qr ؊ 13
8s 2t 2 ؉ s 3 ؉ 8st 2 ؊ 18s 2
11. The volume of a rectangular prism, in cubic meters, is given by
the expression x 3 ؉ 7x 2 ؉ 14x ؉ 8. The volume of a smaller 9. The area of a square, in square yards, is given by the
rectangular prism is given by the expression x 3 ؉ 5x 2 ؉ 6x. expression 4u 4 ؉ 8u 3 ؉ 12u 2 ؉ 8u ؉ 4. The area of a smaller
How much greater is the volume of the larger rectangular prism? square is given by the expression 4u 4 ؉ 4u 3 ؉ 5u 2 ؉ 2u ؉ 1.
How much greater is the area of the larger square?
2x 2 ؉ 8x ؉ 8 cubic meters
4u 3 ؉ 7u 2 ؉ 6u ؉ 3 square yards
12. Sarah has a table with an area, in square inches, given by the
expression of y 2 ؉ 30y ؉ 200. She has a tablecloth with an area, 10. The volume of a rectangular prism, in cubic meters, is given
in square inches, given by the expression of y 2 ؉ 18y ؉ 80. by the expression c 3 ؉ 4c 2 ؉ 3c. The volume of a smaller
She wants the tablecloth to cover the top of the table. What rectangular prism is given by the expression c 3 ؊ c 2 ؊ 2c.
expression represents the number of square inches of additional How much greater is the volume of the larger rectangular prism?
fabric she needs to cover the top of the table?
5c 2 ؉ 5c cubic meters
12y ؉ 120 more square inches of fabric
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
29 Holt Mathematics Copyright © by Holt, Rinehart and Winston.
All rights reserved.
30 Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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