1. Factoring Special Cases
ALGEBRA 1 LESSON 9-7
(For help, go to Lessons 8–4 and 9-4.)
Simplify each expression.
1. (3x)2 2. (5y)2 3. (15h2)2 4. (2ab2)2
Simplify each product.
5. (c – 6)(c + 6) 6. (p – 11)(p – 11) 7. (4d + 7)(4d + 7)
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2. Factoring Special Cases
ALGEBRA 1 LESSON 9-7
Solutions
1. (3x)2 = 32 • x2 = 9x2 2. (5y)2 = 52 • y2 = 25y2
3. (15h2)2 = 152 • (h2)2 = 225h4 4. (2ab2)2 = 22 • a2 • (b2)2 = 4a2b4
5. (c – 6)(c + 6) is the difference of squares. (c – 6)(c + 6) = c2 – 62 = c2 – 36
6. (p – 11)(p – 11) is the square of a binomial. (p – 11)2 = p2 – 2p(11) = p2 – 22p + 121
7. (4d + 7)(4d + 7) is the square of a binomial. (4d + 7)2 = (4d)2 + 2(4d)(7) + 72 = 16d2 + 56d + 49
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3. Factoring Special Cases
ALGEBRA 1 LESSON 9-7
Factor a2 – 16.
a2 – 16 = a2 – 42 Rewrite 16 as 42.
= (a + 4)(a – 4) Factor.
Check: by multiplication.
(a + 4)(a – 4)
a2 – 4a + 4a – 16
a2 – 16
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4. Factoring Special Cases
ALGEBRA 1 LESSON 9-7
Factor 9b2 – 25.
9b2 – 225 = (3b)2 – 52 Rewrite 9b2 as (3b)2 and 25 as 52.
= (3b + 5)(3b – 5) Factor.
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5. Factoring Special Cases
ALGEBRA 1 LESSON 9-7
Factor 5x2 – 80.
5x2 – 80 = 5(x2 – 16) Factor out the GCF of 5.
= 5(x + 4)(x – 4) Factor (x2 – 16).
Check: Multiply the binomials. Then multiply by the GCF.
5(x + 4)(x – 4)
5(x2 – 16)
5x2 – 80
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6. Factoring Special Cases
ALGEBRA 1 LESSON 9-7
Factor each expression.
1. y2 – 18y a2 – 24a + 16
3. p2 – x2 – 225
5. 5m2 – c2 + 20c + 50
(y – 9)2
(3a – 4)2
(p + 13)(p – 13)
(6x + 15)(6x – 15)
5(m + 3)(m – 3)
2(c + 5)2
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