88 CHAPTER R Review of Basic Concepts (b) 298x3y + 3x232xy = 249 # 2 # x2 # x # y + 3x216 # 2 # x # y Factor. = 7x22xy + 3x14222xy Remove all perfect squares from the radicals. = 7x22xy + 12x22xy Multiply. = 17x + 12x222xy Distributive property = 19x22xy Add. (c) 23 64m4n5 - 23 -27m10n14 = 23 64m3n31mn22 - 23 -27m9n121mn22 Factor. = 4mn23 mn2 - 1-3m3n4223 mn2 Remove all perfect cubes from the radicals. = 4mn23 mn2 + 3m3n423 mn2 -1a2 = a = 14mn + 3m3n4223 mn2 S Now Try Exercises 95, 105, and 111. This cannot be simplified further. EXAMPLE 9 Multiplying Radical Expressions Find each product. (a) 225 A 23 - 326B (b) A 27 - 210 B A 27 + 210 B (c) A 22 + 3B A 28 - 5B SOLUTION (a) 225 A 23 - 326B = 225 A 23B - 225 A326B Distributive property = 2215 - 2 # 3 # 25 # 26 2a # 2b = 2ab; Commutative and associative properties = 2215 - 6230 Multiply. (b) A 27 - 210 B A 27 + 210 B = A 27 B 2 - A 210 B 2 Product of the sum and difference of two terms = 7 - 10 A 2a B 2 = a = -3 Subtract. CAUTION The terms 4mn23 mn2 and 3m3n423 mn2 in Example 8(c) are rewritten in the final line using the distributive property. These terms are not alike. Therefore, they cannot be combined.
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