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Name
LESSON
Date
Class
Review for Mastery
12-6 Multiplying Binomials
To multiply a binomial by a binomial, multiply each term of the first binomial
by each term of the second binomial.
(a ! b)(c ! d) " ac ! ad ! bc ! bd
You can remember the product as FOIL: First terms, Outer terms,
Inner terms, and Last terms.
(5x ! 3)(3x # 2)
Multiply the First terms.
(5x)(3x) " 15x 2
Multiply the Outside terms.
Multiply the Inside terms.
(5x)(–2) " #10x
(3)(3x) " 9x
Multiply the Last terms.
Add the products.
Combine like terms.
(3)(–2) " #6
15x 2 #10x ! 9x # 6
15x 2 # x # 6
You can also multiply binomials vertically.
Align the binomials.
5x ! 3
Multiply each term of one
$ 3x # 2
binomial by each term of the
other binomial.
#10x # 6
15x 2 ! 9x
Combine like terms.
15x 2 # x # 6
Multiply.
1. (4x ! 3)(2x ! 5)
2. (7t # 4)(2t ! 3)
3. (3 ! 5b)(2b # 3b 2)
4. (x # 1)(x ! 5)
5. (6m # 3n)(2m ! 3n)
6. (c ! 7)(c ! 1)
7.
6n # 3
$ 3n ! 3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
8.
52
2y ! 4
$ y!6
Holt Mathematics
Practice B
LESSON
12-6 Multiplying Binomials
Practice A
LESSON
12-6 Multiplying Binomials
Multiply.
Multiply.
1. (z ! 3)(z ! 2)
2. (a ! 1)(a ! 2)
z 2 ! 5z ! 6
a 2 ! 3a ! 2
4. (c ! 1)(c " 3)
7. (u " 5v)(3u " v)
8. (–3g + 4)(g – 1)
2
3u " 16uv ! 5v
2
2
"3g ! 7g " 4
"2r " 11rs ! 6s
4k 2 ! 36k ft2
11. A table is placed in a 14 ft # 18 ft room so that there is an equal
amount of space of width s feet all the way around the table.
Write and simplify an expression for the area of the table.
4x 2 ! 160x m 2
12. A rug is placed in a 15 ft # 25 ft room so that there is an
uncovered strip of width h feet all the way around the rug.
Write and simplify an expression for the area of the rug.
252 " 64s ! 4s 2 ft2
12. A circular swimming pool with a radius of 14 ft is surrounded by
a deck with width y feet. Write and simplify an expression for
22
the total area of the pool and the deck. Use !7! for pi.
4h 2 " 80h ! 375 ft2
Multiply.
22
7
616 ! 88y ! !!y 2 ft2
14. (2a ! 1)2
4a 2 ! 4a ! 1
2
15. (e " 3)
Multiply.
13. (r " 2)2
16. (m " 1)(m ! 1)
e 2 " 6e ! 9
14. (2 ! q)2
r 2 " 4r ! 4
m2 " 1
16. (3n " 3)(3n ! 3)
17. (2 ! e)2
k 2 " 2kn ! n 2
19. (2w " z)(2w ! z)
2
4w " z
2
19. (2y ! z)
2
2
4a – b
2
49
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
4. (2w + 1)(–2w – 3)
2. (1 " x)(2 " x)
1
"!
1
5. 2v ! !4! v " !4!
"4w " 8w " 3
81p 2 " 36p ! 4
50
"
6. (3t ! 2)(2t " 3)
1
1
2v " !4!v " !1!
6
6t 2 " 5t " 6
22
!!y 2 ! 132y ! 1,386 m 2
7
(5x ! 3)(3x " 2)
Multiply the First terms.
(5x)(3x) $ 15x 2
Multiply the Outside terms.
(5x)(–2) $ "10x
Multiply the Inside terms.
Multiply the Last terms.
Add the products.
(3)(–2) $ "6
15x 2 "10x ! 9x " 6
Combine like terms.
15x 2 " x " 6
(3)(3x) $ 9x
You can also multiply binomials vertically.
Align the binomials.
Multiply each term of one
8. A rug is placed in a 6 ft # 15 ft hallway so that there is an equal
amount of space of width y feet all the way around the rug. Write
and simplify an expression for the area of the rug.
90 " 42y ! 4y 2 ft2
9. A brick walkway around a circular jacuzzi is 7 ft wide. The radius
of the jacuzzi is 14d ft. Write and simplify an expression for the
total area of the jacuzzi and the brick walkway around the
22
jacuzzi. Use !7! for pi.
5x ! 3
# 3x " 2
binomial by each term of the
other binomial.
"10x " 6
15x 2 ! 9x
Combine like terms.
15x 2 " x " 6
Multiply.
1. (4x ! 3)(2x ! 5)
2. (7t " 4)(2t ! 3)
8x 2 ! 26x ! 15
616d 2 ! 616d ! 154 ft2
14t 2 ! 13t " 12
3. (3 ! 5b)(2b " 3b 2)
Multiply.
p 2 ! 4p ! 4
13. (3c " 3d )(3c ! 3d )
9c 2 " 9d 2
16. (9p " 2q)("2q ! 9p)
81p 2 " 36pq ! 4q 2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
You can remember the product as FOIL: First terms, Outer terms,
Inner terms, and Last terms.
7. A circular swimming pool is surrounded by a deck that is
y meters wide. The radius of the swimming pool is 21 meters.
Write and simplify an expression for the total area of the
22
swimming pool and deck. Use !7! for pi.
10. (p ! 2)2
m 2 " 2m ! 1
(a ! b)(c ! d) $ ac ! ad ! bc ! bd
4c 2 ! 10c ! 4
2
2
21. (m " 1)2
20. (9p " 2)("2 ! 9p)
To multiply a binomial by a binomial, multiply each term of the first binomial
by each term of the second binomial.
3. (2c ! 1)(2c ! 4)
2 " 3x ! x 2
!
16e 2 " 8ef ! f 2
Review for Mastery
LESSON
12-6 Multiplying Binomials
Multiply.
a 2 ! 3a ! 2
18. (4e " f )2
a2 " b2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Practice C
LESSON
12-6 Multiplying Binomials
1. (a ! 1)(a ! 2)
p 2 " 16
17. (a ! b)(a " b)
4y 2 ! 4yz ! z 2
20. (2a ! b)(2a " b)
15. (p ! 4)(p " 4)
4 ! 4q ! q 2
9n 2 " 9
18. (k " n)2
4 ! 4e ! e 2
2a 2 ! 5ab ! 2b 2
18 " 38m ! 4m 2 in.2
11. Write and simplify an expression for the area of a brick walkway
of width x m around a 30 m by 50 m yard.
e 2 ! 2e ! 1
9. (2a ! b)(a ! 2b)
3c 2 – 5cd – 2d 2
10. A box is formed from a 1 in. by 18 in. piece of cardboard by
cutting a square with side length m inches out of each corner
and folding up the sides. Write and simplify an expression for the
area of the base of the box.
10. Write an expression for the area of a cement walkway of width k
ft around an 8 ft by 10 ft jacuzzi.
13. (e ! 1)2
2t 2 ! 2t " 4
8. (3c ! d)(c " 2d)
"6g 2 ! 11g " 4
2
6. (t ! 2)(2t " 2)
3v 2 " 2v " 1
7. ("3g ! 4)(2g " 1)
9. (–2r + s)(r + 6s)
2
4x 2 ! 10x ! 4
5. (3v ! 1)(v " 1)
w 2 " 2w " 3
4r 2 " 1
3. (2x ! 1)(2x ! 4)
2 " 3y ! y 2
4. (w ! 1)(w " 3)
6. (2r ! 1)(2r " 1)
9v 2 " 12v ! 3
2. (1 " y)(2 " y)
z 2 ! 3z ! 2
3b 2 ! 4b ! 1
5. (3v – 1)(3v – 3)
c 2 " 2c " 3
1. (z ! 1)(z ! 2)
3. (b ! 1)(3b ! 1)
11. (2 " k)2
4 " 4k ! k 2
14. (2a ! b)(2a " b)
4a 2 " b 2
17. (2m " 3b)2
4m 2 " 12bm ! 9b 2
51
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
x 2 ! 4x " 5
5. (6m " 3n)(2m ! 3n)
d 2 " 196
!
4. (x " 1)(x ! 5)
6b ! b 2 " 15b 3
12. (d ! 14)(d " 14)
6. (c ! 7)(c ! 1)
12m 2 ! 12mn " 9n 2
"
1
1
15. !2!c ! d (!2!c " d )
7.
1
!!c 2 " d 2
4
c 2 ! 8c ! 7
6n " 3
# 3n ! 3
8.
#
18n 2 ! 9n " 9
18. (9a ! 3b)(9a " 3b)
2y ! 4
y!6
2y 2 ! 16y ! 24
81a 2 " 9b 2
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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Holt Mathematics
Holt Mathematics