Download Multiply Bino Puzzle

Name
LESSON
Date
Class
Puzzles, Twisters & Teasers
12-6 Back It Up!
What do you have when a row of rabbits steps backwards?
To find the answer, find each product in Column 1 and match it
to the correct expression in Column 2. Then, write the letter
above the corresponding exercise number.
Column 1
Column 2
1. (x ! 4)2
A x 2 ! 4x " 32
2. (x ! 3)(x ! 6)
C x 2 ! 9x ! 18
3. (x ! 8)(x " 4)
D x 2 " 16
4. (x ! 4)(x " 4)
E 6x 2 " 2x " 20
5. (x " 9)(x " 2)
G 9x 2 " 30x ! 25
6. (x " 16)(x ! 2)
H x 2 " 14x " 32
7. (2x " 5)(3x ! 4)
I
8. (6x ! 10)(x " 2)
L x 2 ! 8x ! 16
9. (3x " 5)2
N x 2 " 11x ! 18
R 9x 2 " 25
10. (3x " 5)(3x ! 5)
3
6
10
3
8
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Copyright © by Holt, Rinehart and Winston.
All rights reserved.
6x 2 " 7x " 20
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Holt Mathematics
Challenge
LESSON
12-6 Multiplication Tables
Problem Solving
LESSON
12-6 Multiplying Binomials
Example: (x # 3)(x " 2)
You can use a table to multiply binomials.
Label each column with a term from one of the
binomials, and label each row with a term from
the other binomial of the coefficients.
Then multiply the same as in a multiplication table
(column ! row). Finish by combining like
terms in the product.
Use the given tables to find each product.
x
"2
x
3
x2
3x
"2x
Write and simplify an expression for the area of each polygon.
"6
2
2
x # 3x " 2x " 6 $ x # x " 6
2. (3m # 5)2
1. (x " 4)(x " 5)
x
"4
x
x2
"4x
"5
"5x
20
3m
5
3m
9m 2
15m
5
15m
25
x 2 " 9x # 20
2h
1
7p
"q
2h 2
h
p
7p 2
"pq
"4
"8h
"4
6q
42pq
"6q 2
2h 2 " 7h " 4
7p 2 # 41pq " 6q 2
2
5. (3a # 4b)
3a
4b
5w
"10
9a 2
12ab
2w
10w 2
"20w
4b
12ab
16b 2
"v
"5wv
10v
9a 2 # 24ab # 16b 2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
n 2 # n " 20
Area
2.
rectangle
length: (3y # 3); width: (2y " 1)
6y 2 # 3y " 3
3.
triangle
base: (2b " 5); height: (b 2 # 2)
b 3 " !2!b 2 # 2b " 5
4.
square
side length: (m # 13)
m 2 # 26m # 169
5.
square
side length: (2g " 4)
4g 2 " 16g # 16
6.
circle
radius: (3c # 2)
5
(9c 2 # 12c # 4)!
8. Three consecutive odd integers
are represented by the expressions,
x, (x # 2) and (x # 4). Which
expression gives the product of the
three odd integers?
F x3 # 8
G x 3 # 6x 2 # 8x
!
H x 3 # 6x 2 # 8
J x 3 # 2x 2 # 8x
10. Which expression gives the product
of (3m # 4) and (9m " 2)?
F 27m 2 # 30m " 8
!
G 27m 2 # 42m " 8
H 27m 2 # 42m # 8
J 27m 2 # 30m # 8
9. A square garden has a side length of
(b " 4) yards. Which expression
shows the area of the garden?
A 2b " 8
B b 2 # 16
C b 2 " 8b " 16
D b 2 " 8b # 16
!
6. (5w " 10)(2w " v)
3a
length: (n # 5); width: (n " 4)
7. A photo is 8 inches by 11 inches.
A frame of width x inches is placed
around the photo. Which expression
shows the total area of the frame
and photo?
A x 2 # 19x # 88
B 4x 2 # 38x # 88
!
C 8x # 38
D 4x # 19
4. (7p " q)(p # 6q)
h
Dimensions
rectangle
Choose the letter of the correct answer.
9m 2 # 30m # 25
3. (2h # 1)(h " 4)
Polygon
1.
10w 2 " 5wv " 20w # 10v
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Holt Mathematics
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Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Reading Strategies
LESSON
12-6 Use Graphic Aids
Holt Mathematics
Puzzles, Twisters & Teasers
LESSON
12-6 Back It Up!
This chart can help you remember how to multiply binomials.
What do you have when a row of rabbits steps backwards?
How to Multiply Binomials
Special Products of Binomials
FIRST, OUTER, INNER, LAST
First
Last
(a " b)2 # (a ! b)(a ! b) # a 2 ! 2ab ! b 2
Example: (x ! 4)2 # x 2 ! 2(4)(x) ! 42
# x 2 ! 8x ! 16
(a " b)(c " d)
Inner
Outer
ac " ad " bc " bd
To find the answer, find each product in Column 1 and match it
to the correct expression in Column 2. Then, write the letter
above the corresponding exercise number.
Column 1
1. (x # 4)
A x 2 # 4x " 32
Example: (x " 6)2 # x 2 " 2(6)(x) ! 62
# x 2 " 12x ! 36
2. (x # 3)(x # 6)
C x 2 # 9x # 18
3. (x # 8)(x " 4)
D x 2 " 16
4. (x # 4)(x " 4)
E 6x 2 " 2x " 20
5. (x " 9)(x " 2)
G 9x 2 " 30x # 25
6. (x " 16)(x # 2)
H x 2 " 14x " 32
7. (2x " 5)(3x # 4)
I
8. (6x # 10)(x " 2)
L x 2 # 8x # 16
9. (3x " 5)2
N x 2 " 11x # 18
2
(a " b)(a # b) # a 2 " b 2
The Commutative Property states that it
does not matter in which order you write
the addends.
Column 2
(a # b)2 # (a " b)(a " b) # a 2 " 2ab ! b 2
Example: (x ! 7)(x " 7) # x 2 " 72
# x 2 " 49
Use the information in the chart to answer the
following questions.
1. What do the letters FOIL represent?
first, outer, inner, last
2. Does it matter in which order you write the addends? Why or why not??
No; the Commutative Property guarantees that ac # ad $ ad # ac, etc.
3. When finding the special product of (a ! b)2, how many terms will you always have?
R 9x 2 " 25
10. (3x " 5)(3x # 5)
three
4. When finding the special product of (a " b)2, why is the last term positive?
because negative b times negative b is positive b 2
6x 2 " 7x " 20
A
R
E
C
E
D
I
N
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3
10
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2
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5
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A
R
E
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3
10
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1
7
5
8
5. Why do you get only two terms when you multiply binomials in the special form
(a ! b)(a " b)?
The middle two terms are ab and "ab , which cancel each other out.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
55
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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Holt Mathematics
Holt Mathematics