1. Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
(For help, go to Lessons 8–4 and 9-3.)
Simplify.
1. (7x)2 2. (3v)2 3. (–4c)2 4. (5g3)2
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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2. Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
Solutions
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
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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3. 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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4. 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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5. 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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6. Multiplying Special Cases
ALGEBRA 1 LESSON 9-4
Find each square.
1. (y + 9)2 2. (2h – 7)2
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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