Extra Practice Answers
BLM 7GR
Chapter 7 Get Ready
1. a) x2 + 2x + 4 b) 2y + 1 + 3x2
2. a)
c) 4x – xy + 5
d) 3y2 – 2x – 6
b)
1
x2
x
1
x
1
–y 2
1
c)
–y 2
x
x
x
–1 –1
–1 –1
–1
d)
x2
x2
–y 2
–xy
–y 2
–xy
–y 2
–y 2
–y 2
–1 –1
–y –y –1 –1
–1
x2
x2
–y 2
e)
x
f)
–y 2
–y 2
–y 2
–y 2
x
xy
xy
xy
x
xy
x
–xy
1
1
1
3. Answers may vary but students need to use the zero principle in order to draw more than 7 tiles.
4. a) –y
–y
One pair of y-tiles and one pair of x-tiles each combined to make zero.
b) 4x2 – 2y
x2
x2
x2
x2
–y –y
The 2x2 and 2x2 values combine to make 4x2 and the two –y-values combine to make –2y.
c) –3 + 2xy
xy
–1
xy
–1
–1
The positive and negative one tiles combine to make –3 using the zero principle and the 4 positive xy-values
combine with two negative xy-values to make 2xy using the zero principle.
d) 7x + 5y
y y y y y
x
x
x
x
x
x
x
The 8 positive x-tiles and 1 negative x-tile combine to make 7x using the zero principle.
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e) –3xy – 5x2 + 1
–xy
–x2
–x2
–x2
1
–xy
–xy
–x2
–x2
The 3 negative one tiles with the 2 negative one tiles make 1 using the zero principle. The 2 positive xy-tiles and 5
negative xy-tiles combine to make 3xy using the zero principle.
5.
Term
a) 3y
b) –x2
c)
1
x
2
Literal
Coefficient
y
x2
x
Numerical
Coefficient
3
–1
y2
xy
2
–10
d) 2y2
e) –10xy
6. a) iv
b) ii
c) iii
1
2
d) i
e) ii
f) iii or i
g) i
7. Even though it is not written, the numerical coefficient is –1 because you can represent –y2 with one white
(orange) square. It is not necessary to write –1y2 but if one had 2 white orange squares, one would have to write
–2y2.
8. a) No because –2y and –2y2 are different.
b) No because 5 and –5 are different.
–xy
x
x
x
x
1
–y –y
1
–1
1
–xy
–xy
–y2
–y2
1
x
x
x
x
9. a) (1 × 27, 3
c) (1 × 13)
× 9)
8
1
10. a)
5
11. a) 7
b)
–1 –1
–x –1 –1
3
b) 3
1
1
1
–x 1
1
1
1
–xy
b) (1
d) (1
c)
5
4
c) 4
× 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8)
× 39, 3 × 13)
d)
1
2
d) 2
e) 9
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Extra Practice Answers
BLM 7.1
7.1 Add and Subtract Polynomials
1. a) 5r
b) 5r
c) 2w + 2.5x
2. a) 3x
b) 5x
3. a) 6x + 3
b) –9 – 4y + 3x
d) 4z + 6y
c) 8x2 – xy
d) 8z + 2z2 – 6
e) 4m2 + 9 – 2mn
f)
3
4
y + x g) s – 2
4
3
4.
Expression A
+
a) x2 + 3x + 5
b) 2xy – y2
c) x2 – 4x + 6
+
+
+
Expression B
x2 + 2x – 6
x – 3xy + y
–4 – x + x2
Final
Expression
2x2 + 5x – 1
–xy – y2 + x + y
2x2 – 5x + 2
5. a)
b)
–1 –1 –1
y y y y y y y y –y –y –y –y –y
x2
x2
x
x
x
xy
x –x
–xy
x2
x2
2x2 + 4x – xy
d)
8y – 1
c)
x
xy
xy
xy
–xy
xy
–xy
xy
–xy
x
x
x
x
–x2
x2
1
–1
1
–1
1
1
–1
1
–1
1
1
–1
1
–1
1
1
–1
1
–1
1
1
–1
1
–1
–x2
–x2
x + x2 – 6
5xy + 8
6. a) –5x + 5
b) y + 3
c) 3x2 – 14x + 3
7. a) Symbolically x + 2x – 3 = 3x – 3
Pictures
d) m2 + 2mn
b) Symbolically 2x – 3 – x = x – 3
Pictures
1
x
x
x
1
1
1
x
x
1
1
8. a) y + 3y – 5 = 4y – 5
b) 4y – 5 = 4(20) – 5; equals $75
c) 4y – 5 = 4(5.50) – 5; equals $17
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9. a)
b) 2y + 8y – 3 + 2y + 8y – 3 = 20y – 6
c) 20y – 6 = 20(2 m) – 6
= 34 m
2y
8y – 3
8y – 3
2y and 8y –2y3
10. 4xy represents 4 grey rectangles and 4x + y represents 4 green rectangles and 1 orange rectangle, and they are
unlike terms that cannot be added together.
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Extra Practice Answers
BLM 7.2
7.2 Common Factors
1. a) 4y + 8 = 4(y + 2)
b) 8x + 6y = 2(4x + 3y)
2. a) 2(2x + 6) and 4(x + 3) (factored fully)
x
x
1
1
1
1
1
1
x
x
1
1
1
1
1
1
x
1
1
1
x
1
1
1
x
1
1
1
x
1
1
1
c) 4x2 + 6xy = 2x (2x + 3y)
b) 2(4y + 8) and 4(2y + 4) and 8(y + 2) (factored fully)
y
y
y
y
y
y
y
y
y
y
1
1
1
1
1
1
1
1
y
y
y
y
1
1
1
1
1
1
1
1
c) 3(x + 3) (factored fully)
x
1
1
1
x
1
1
1
x
1
1
1
3. a) Sharing two groups of x + 4
x
1
1
1
x
1
y
1
1
y
1
1
y
1
1
1
1
1
1
1
1
1
1
1
1
y
y
1
1
1
1
y
y
1
1
1
1
y
y
1
1
1
1
y
y
1
1
1
1
1
1
1
1
1
1
1
x
1
1
1
1
x
1
1
1
1
Area = 5(y + 2)
y
1
y
y
Area = 2(x + 4)
1
b) Sharing five groups of y + 2
y
d) 8x2 + 10x = 2x (4x + 5)
1
1
1
y
1
1
y
1
1
y
1
1
y
1
1
y
1
1
4. One cannot equally divide the terms into 3x equal groups.
Therefore one has to use an area model and one will have a rectangle that measures 3x(x + 2)
x2
x2
x2
x
x
x
x
x
x
5. a) 10(2x + 5) GCF = 10
b) 3(x + 12) GCF = 3
c) 8(a – 8) GCF = 8
d) b(b + 7) GCF = b
e) 5y(y + 8) GCF = 5y
f) 7m(1 + 2n) GCF = 7m
g) 6(a2 + 2a + 3) GCF = 6
h) 3r(3r + 2t – 4) GCF = 3r i) c(–3a + 5b – c) GCF = c
j) –2x(x2 + 4x + 2) GCF = –2x k) 3(a2 – 4ab + 4b2) GCF = 3
6. The GCF between x2 and 3 is 1. The area model will not make a rectangle.
7. a)
b) x + 2
x2
x2
x2
x2
x
x
x
x
x
x
x
x
c) 10x + 4
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1
1
Extra Practice Answers
BLM 7.3
7.3 Multiply a Monomial by a Polynomial
1. a) 2x (x + 1)
b) x(x + 3)
c) 3(x + 2)
d) x(2x + 2)
b) 2xy + 4y2
2. a) 3x + 3
x
1
x
1
x
1
d) 6xy + 2x2
c) 0 (no drawing)
xy
y2
y2
xy
y2
y2
e) 2x2 + 4xy + 6x
f) 9y2 + 3xy + 6y
xy
xy
xy
xy
xy
y2
y2
y2
y y
xy
xy
xy
xy
xy
y2
y2
y2
y y
xy
xy
x2
x2
xy
y2
y2
y2
y y
x
x
x2
x2
3. a) 5p + 15q
b) kn – mn
e) 6a2 + 6ab – 9a – 4ab2
4. a) b6 – 7b4 + 5b = –38
c) ac – bc + 4c
f) 8p2 + 16p –18
b) –3c3 + 4b2c – 4b = –136
d) –6x – 4
g) 16x2 – 4xy –16x + 4y2
c) –25a = –75
5. 3(2x + y) = 6x + 3y
x
x
y
x
x
y
x
x
y
6. 2m + 4(m + 4) = 6m + 16 dollars
7. a) Perimeter = 28e; Area = 34e2
b) Perimeter = 14d + 32c; Area = 72c2d2
8. The number of terms in the answer will depend on the number of terms in the polynomial. If there are two terms
in the polynomial, the answer will contain two terms; if there are three terms, the answer will contain three terms,
etc., provided that there are no like terms to be combined.
3x(4x + 2y) = 12x2 + 6xy (two terms)
2y(2x + 2 – 3y) = 4xy + 4y – 6xy (three terms)
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Extra Practice Answers
BLM 7.4
7.4 Multiply Two Binomials
1. a) (y + 4)(y + 2) = y2 + 6y + 8
b) (x + 1)(x + 1) = x2 + 2x + 1
2. a) (3y + 4)(2y + 1) = 6y2 + 11y + 4
b) (2x + 1)(2y + 2) = 4xy + 2y + 4x + 2
x
x
1
y
xy
xy
y
y y y y
y
xy
xy
y
1 1 1 1
1
x
x
1
1
x
x
1
yy
yy
y
1
1 1
1 1
1 1
1
y
y2
y2
y2
y y y y
y
y2
y2
y2
1
y
y
y
c) x2 + 3x + 2
d) 2y2 + 7y + 6
x
e) 16 + 8y + y2
y y
y2
y y y y
y2
y y
y
y
y
y
1
1
1
1
y
y
y
1 1
1 1
1 1
y2
x2
c) (y + 2x)(y + x) = y2 + 3xy + 2x2
x x
1
1
3. a) –6 – 2c + 3d + cd
e) –81p2 + 4
b) 10k – k2 – 9
f) –3m2 – 19m + 72
c) a2 + 2ab + b2
g) 12 + 6d – 6d2
1
1
1
1
1
1
1
1
1
1
1
1
d) m2 – 2mn + n2
h) 2m3 + m2n + 2mn2 + n3
4. a) i) y2 + 4y + 4
ii) y2 – 4y + 4
iii) y2 – 4
2
2
b) i) m + 12m + 36 ii) m – 12m + 36 iii) m2 – 36
• When you multiply two binomials where each term is positive, the term that is not squared will be positive.
• When you multiply two binomials where one term is negative, the term that is not squared will be negative.
• When you multiply two binomials where one term is negative and the second binomial is the opposite, the term
that does not have a square will be eliminated.
5. 8n2 – 14n – 15
6. a) (x – 1)(x – 4)
b) (p + 3)(p – 8)
c) (w – 7)(w – 5)
d) (y – 7)(y + 4)
7. a) (x + 4)
b) (y – 2)
c) (z + 3)
d) (c + 8)
8. a) 3x2 – 10x
b) –x2 – 8x + 5
c) 2y2 – 44
d) 3x3 + 5x2 – 21x + 10
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This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.
Extra Practice Answers
BLM 7.5
7.5 Polynomial Division
1. a) x + 2
b) –2x – 3
c) 2y – x
d) 2y – 3
2. a) x + 2
b) 1 + 2y
c) 5x + 2
d) 4y + 2
3. a) 2a – 2
b) 13y + 1
c) 2n – m
d) c + 4c3 + 6c2 – 2
4. a) 2y –
1
2
b) –
1
2
w+
1
10
c)
1
4
h–
8
k
1
r+1
2
b) –5n2 + n – 3
c) –
7. a) 2p
b) 6eg
c) 8ab2
8. a) 11x + 1
b) 35x2 + 5x
5. a) 10x + 4
1
e) –3a3b3 + ab + 8b
d) –2y + 12
6. x2y + 2x2
d) d – 2
e) 4xy + 2x
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Extra Practice Answers
BLM 7.6
7.6 Apply Algebraic Modelling
1. a) x ÷ 3
b) x2 + 7
c) x + x2
d) 3x – 4
e) x(4 + y)
2. a) i) (x + 2)5 ii) x + 2(5)
b) yes
c) (x + 2)5 = 25 and x + 2(5) = 13
d) Answers will vary. Four times a number, divided by 2; four times a number divided by two.
x
4x ÷ 2 or 4 ⎛⎜ ⎞⎟ both give the same answer. No, it depends on the order of operations.
⎝ 2⎠
3. a) x ÷ 30
b) $34.99 + $5.25 = $40.24
$40.24 ÷ 30 = $1.34
4. 13x
5. 20 – 2x
6. a) Sales = 10.75a + 8.75y + 5.50c + 5g
b)
Total
Number of tickets sold
Sales ($)
Adult
Youth
Child
992.25
35
52
12
971.25
25
58
20
1338
57
61
13
1702.75
93
52
6
1403.25
47
38
51
7. a) 4h + 10
8. a) Area = l
b)
Area (cm2)
62.5
162
28.125
9. a) 0.195x
+64
19
17
24
43
57
b) 6.5 h
× w, where l is the length and w is the width.
Length (cm)
5
18
6.25
Width (cm)
12.5
9
4.5
b) 0.195(475) = $92.63
c) $678.32
d) $678.32 – $475 = $203.32
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Extra Practice Answers
BLM 7R
Chapter 7 Review
1. a) –m – 2
b) 3x2 + 3x + 1
c) 10y3 – 8y + 7
d) 4a + b
e) –10p + 4q
2. a) 11b
b) (2a – 5)
c) –8xz
d) (–5mn)
e) (2x + 3)
f) m
3. Examples will vary. It is easier to use the sharing model when the common factor is a number, and the area
model when the common factor is literal.
4. There are several possibilities:
1(10xy), 2(5xy), 5(2xy), 10(xy), x(10y), 2x(5y), 5x(2y), 10x(y), y(10x), 2y(5x), 5y(2x), 10y(x), 2(5)(x)(y), 2(5)(xy),
10(x)(y), 1(10)(xy), 2(5x)(y), 2(x)(5y)
5. a)(2x + 2)(x + 2) = 2x2 + 6x + 4
b) 3ab2
6. a) 5xy
7. a) 5x
b) 5x2 + 16x
2
e) –7x – 4xy – 12x
8. a) 5s
b) (x + y)(3y + 5) = 3xy + 3y2 + 5x + 5y
c) –3y2 + 5y
f) 2y2 – 44
b)15a – 7b + 6
c)
3
2
x+3–
d) 7m2 – 26m + 24
g) 3x3 + 5x2 – 21x + 10
9
2
x2y
d) 4b
9. 80x2 – 16xy
10. a) 8x + 10
b) 3x2 + 7x + 4
c) Area = 52 cm2; Perimeter = 34 cm
11. a) 4t(t2 + 2)
b) 5mn(3m2 + 5mn – 4)
c) 3x(4x + 3)
d) 11(2x + y)
e) 3b(–b2 + 2b – 4)
12. Cost = 4.50 + 0.80x
Total Fare
($)
$24.50
$38.90
$12.50
$34.10
Distance
(km)
25
43
10
37
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Extra Practice Answers
BLM 7PT
Chapter 7 Practice Test
1. B
2. D
3. C
4. C
5. C
6. a) 4x(2x + 1)
b) (5 + x)(5 + x)
Answers may vary but the first one may be seen as easier to draw an area model as it is a monomial that is common
between both terms, and in the second question it is a binomial which may not be as evident.
7. There is no common factor between the terms and there are no two binomials that will multiply to give the
equation.
8. a) 3x2 – 10x
e) 2x – 3
9. a) Area = nt – 3a2
b) –x2 – 8x + 5
f) 5a – 3b + 4
c) 2y2 – 44
g) 4b
d) 3x3 + 5x2 – 21x + 10
b) Area = (5)(12) – 3(1.5)2
Area = 53.25 m2
10. a) i) Area = 35y2 – 20y; Perimeter = 24y – 8
ii) Area = 14xy + 9y; Perimeter = 8x + 6 + 8y
b) Area = 480; Perimeter = 88; Area = 148; Perimeter = 54
11. a) xy + 2y + x + 2
xy
y
y
x
1
1
b) 6x2 + 14x + 4
x2
x2
x2
x
x2
x2
x2
x
x
x
x
1
x
x
x
1
x
x
x
1
x
x
x
1
12. a) Salary = 7.50h + 0.02p + 0.05w
h = hours, p = precious jewels and gold, w = watches
13. a) Score = 3w + 2t + l
w = win, t = tie, and l = loss
b) $192.50
b) Lions: 20 points
Eagles: 19 points
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