# Factoring Special Cases - Gateway School District ALGEBRA ALGEBRA 1 1 LESSON LESSON 9-7 9-7 Factoring Special Cases (For help, go to Lessons 84 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) 5-5

7. (4d + 7)(4d + 7) ALGEBRA ALGEBRA 1 1 LESSON LESSON 9-7 9-7 Factoring Special Cases 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) + 112 = 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 5-5 ALGEBRA ALGEBRA 1 1 LESSON LESSON 9-7 9-7 Factoring Special Cases Factor a2 16. a2 16 = a2 42 = (a + 4)(a 4) Rewrite 16 as 42. Factor. Check: by multiplication. (a + 4)(a 4) a2 4a + 4a 16 a2 16 5-5

ALGEBRA ALGEBRA 1 1 LESSON LESSON 9-7 9-7 Factoring Special Cases Factor 9b2 25. 9b2 225 = (3b)2 52 = (3b + 5)(3b 5) Rewrite 9b2 as (3b)2 and 25 as 52. Factor. 5-5 ALGEBRA ALGEBRA 1 1 LESSON LESSON 9-7 9-7

Factoring Special Cases 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 5-5 ALGEBRA ALGEBRA 1 1 LESSON LESSON 9-7 9-7 Factoring Special Cases Factor each expression.

1. y2 18y + 81 2. 9a2 24a + 16 (y 9)2 3. p2 169 (3a 4)2 4. 36x2 225 (p + 13)(p 13) 5. 5m2 45 (6x + 15)(6x 15) 6. 2c2 + 20c + 50 5(m + 3)(m 3) 2(c + 5)2 5-5