Multiplying Binomials

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Multiplying Binomials
ALGEBRA 1 LESSON 9-3
(For help, go to Lesson 9-2.)
Find each product. 1. 4r(r 1) 2. 6h(h2 8h
3) 3. y2(2y3 7) Simplify. Write each answer in
standard form. 4. (x3 3x2 x) (5x2 x
1) 5. (3t3 6t 8) (5t3 7t 2)
6. w(w 1) 4w(w 7) 7. 6b(b 2) b(8b
3) 8. m(4m2 6) 3m2(m 9) 9. 3d2(d3 6)
d3(2d2 4)
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Multiplying Binomials
ALGEBRA 1 LESSON 9-3
1. 4r(r 1) 4r(r) 4r(1) 4r 2
4r 2. 6h(h2 8h 3) 6h(h2) 6h(8h) 6h(3)
6h3 48h2 18h 3. y2(2y3 7) y2(2y3) 7y2
2y5 7y2 4. x3 3x2 x 5. 3t3 6t 8
5x2 x 1 5t3 7t 2 x3 8x2
2x 1 8t3 t 6
Solutions
6. w(w 1) 4w(w 7) 7. 6b(b 2) b(8b
3) w(w) w(1) 4w(w) 4w(7) 6b(b)
6b(2) b(8b) b(3) w2 w 4w2 28w 6b2
12b 8b2 3b (1 4)w2 (1 28)w (6
8)b2 (12 3)b 5w2 27w 2b2 15b
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Multiplying Binomials
ALGEBRA 1 LESSON 9-3
Solutions (continued)
8. m(4m2 6) 3m2(m 9) m(4m2) m(6)
3m2(m) 3m2(9) 4m3 6m 3m3 27m2 (4
3)m3 27m2 6m 7m3 27m2 6m 9. 3d2(d3
6) d3(2d2 4) 3d2(d3) 3d2(6) d3(2d2)
d3(4) 3d5 18d2 2d5 4d3 (3 2)d5
4d3 18d2 d5 4d3 18d2
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Multiplying Binomials
ALGEBRA 1 LESSON 9-3
Simplify (2y 3)(y 2).
(2y 3)(y 2) (2y 3)(y) (2y
3)(2) Distribute 2y 3.
2y2 3y 4y 6 Now distribute y and 2.
2y2 y 6 Simplify.
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Multiplying Binomials
ALGEBRA 1 LESSON 9-3
Simplify (4x 2)(3x 6).
The product is 12x2 18x 12.
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Multiplying Binomials
ALGEBRA 1 LESSON 9-3
Find the area of the shaded region. Simplify.
area of outer rectangle (3x 2)(2x 1)
area of hole x(x 3)
area of shaded region area of outer rectangle
area of hole
(3x 2)(2x 1) x(x 3) Substitute.
6x2 3x 4x 2 x2 3x Use FOIL to
simplify (3x 2) (2x 1) and the Distributive
Property to simplify x(x 3).
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Multiplying Binomials
ALGEBRA 1 LESSON 9-3
Simplify the product (3x2 2x 3)(2x 7).
21x2    14x    21   Multiply by 7.
6x3    4x2     6x Multiply by 2x.
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Multiplying Binomials
ALGEBRA 1 LESSON 9-3
(continued)
Method 2 Multiply using the horizontal method.
The product is 6x3 17x2 8x 21.
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Multiplying Binomials
ALGEBRA 1 LESSON 9-3
Simplify each product using any method. 1. (x
3)(x 6) 2. (2b 4)(3b 5) 3. (3x 4)(3x2
x 2) 4. Find the area of the shaded region.
x2 3x 18
6b2 22b 20
9x3 9x2 2x 8
2x2 3x 1
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Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
(For help, go to Lessons 84 and 9-3.)
Simplify. 1. (7x)2 2. (3v)2 3. (4c)2 4. (5g3)2 M
ultiply to find each product. 5. (j 5)(j
7) 6. (2b 6)(3b 8) 7. (4y 1)(5y
2) 8. (x 3)(x 4) 9. (8c2 2)(c2
10) 10. (6y2 3)(9y2 1)
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Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
1. (7x)2 72 x2 49x2 2. (3v)2 32 v2
9v2 3. (4c)2 (4)2 c2 16c2 4. (5g3)2 52
(g3)2 25g6
Solutions
5. (j 5)(j 7) (j)(j) (j)(7) (5)(j)
(5)(7) j2 7j 5j 35 j2 12j 35
6. (2b 6)(3b 8) (2b)(3b) (2b)(8)
(6)(3b) (6)(8) 6b2 16b 18b 48
6b2 34b 48
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Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
Solutions (continued)
7. (4y 1)(5y 2)) (4y)(5y) (4y)(2)
(1)(5y) (1)(2) 20y2 8y 5y 2 20y2
3y 2
8. (x 3)(x 4) (x)(x) (x)(-4) (3)(x)
(3)(4) x2 4x 3x 12 x2 x 12
9. (8c2 2)(c2 10) (8c2)(c2) (8c2)(10)
(2)(c2) (2)(10) 8c4 80c2 2c2 20
8c4 78c2 20
10. (6y2 3)(9y2 1) (6y2)(9y2) (6y2)(1)
(3)(9y2) (3)(1) 54y4 6y2 27y2 3
54y4 21y2 3
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Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
a. Find (y 11)2.
(y 11)2 y2 2y(11) 72 Square the binomial.
y2 22y 121 Simplify.
b. Find (3w 6)2.
(3w 6)2 (3w)2 2(3w)(6) 62 Square the
binomial.
9w2 36w 36 Simplify.
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Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
Among guinea pigs, the black fur gene (B) is
dominant and the white fur gene (W) is recessive.
This means that a guinea pig with at least one
dominant gene (BB or BW) will have black fur. A
guinea pig with two recessive genes (WW) will
have white fur.
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Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
(continued)
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Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
a. Find 812 using mental math.
812 (80 1)2
b. Find 592 using mental math.
592 (60 1)2
602 2(60 1) 12 Square the binomial.
3600 120 1 3481 Simplify.
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Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
Find (p4 8)(p4 8).
(p4 8)(p4 8) (p4)2 (8)2 Find the
difference of squares.
p8 64 Simplify.
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Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
Find 43 37.
43 37 (40 3)(40 3) Express each factor
using 40 and 3.
402 32 Find the difference of squares.
1600 9 1591 Simplify.
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Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
Find each square. 1. (y 9)2 2. (2h
7)2 3. 412 4. 292 5. Find (p3 7)(p3
7). 6. Find 32 28.
y2 18y 81
4h2 28h 49
1681
841
p6 49
896
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