By Ron Larson
This market-leading textual content maintains to supply scholars and teachers with sound, constantly dependent factors of the mathematical options. Designed for a two-term direction, the hot 8th variation keeps the positive factors that experience made Algebra and Trigonometry a whole resolution for either scholars and teachers: fascinating purposes, state of the art layout, and leading edge know-how mixed with an abundance of conscientiously written routines.
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Extra resources for Algebra and Trigonometry (Eighth Edition)
Now try Exercise 97. Sometimes it is necessary to rationalize the numerator of an expression. 5 you will use the technique shown in the next example to rationalize the numerator of an expression from calculus. WARNING / CAUTION Do not confuse the expression Ί5 ϩ Ί7 with the expression Ί5 ϩ 7. In general, Ίx ϩ y does not equal Ίx ϩ Ίy. Similarly, Ίx 2 ϩ y 2 does not equal x ϩ y. Example 15 Ί5 Ϫ Ί7 2 Rationalizing a Numerator ϭ Ί5 Ϫ Ί7 Ί5 ϩ Ί7 и Ί5 ϩ Ί7 2 Multiply numerator and denominator by conjugate of numerator.
94. 95. 96. 97. 98. 99. 100. ͑x ϩ 3͒͑x ϩ 4͒ 64. ͑x Ϫ 5͒͑x ϩ 10͒ ͑3x Ϫ 5͒͑2x ϩ 1͒ 66. ͑7x Ϫ 2͒͑4x Ϫ 3͒ ͑x ϩ 10͒͑x Ϫ 10͒ 68. ͑2x ϩ 3͒͑2x Ϫ 3͒ ͑x ϩ 2y͒͑x Ϫ 2y͒ 70. ͑4a ϩ 5b͒͑4a Ϫ 5b͒ 2 ͑2x ϩ 3͒ 72. ͑5 Ϫ 8x͒ 2 ͑x ϩ 1͒ 3 74. ͑x Ϫ 2͒ 3 ͑2x Ϫ y͒ 3 76. ͑3x ϩ 2y͒ 3 3 2 ͑4x Ϫ 3͒ 78. ͑8x ϩ 3͒2 ͑x 2 Ϫ x ϩ 1͒͑x 2 ϩ x ϩ 1͒ ͑x 2 ϩ 3x Ϫ 2͒͑x 2 Ϫ 3x Ϫ 2͒ ͑Ϫx2 ϩ x Ϫ 5͒͑3x2 ϩ 4x ϩ 1͒ ͑2x2 Ϫ x ϩ 4͒͑x2 ϩ 3x ϩ 2͒ ͓͑m Ϫ 3͒ ϩ n͔͓͑m Ϫ 3͒ Ϫ n͔ ͓͑x Ϫ 3y͒ ϩ z͔͓͑x Ϫ 3y͒ Ϫ z͔ ͓͑x Ϫ 3͒ ϩ y͔2 86. ͓͑x ϩ 1͒ Ϫ y͔2 2 2 ͑2r Ϫ 5͒͑2r ϩ 5͒ 88.
Factor the expression. EXPLORATION TRUE OR FALSE? In Exercises 149 and 150, determine whether the statement is true or false. Justify your answer. 149. The difference of two perfect squares can be factored as the product of conjugate pairs. 150. The sum of two perfect squares can be factored as the binomial sum squared. 151. ERROR ANALYSIS Describe the error. 9x Ϫ 9x Ϫ 54 ϭ ͑3x ϩ 6͒͑3x Ϫ 9͒ 2 ϭ 3͑x ϩ 2͒͑x Ϫ 3͒ 152. THINK ABOUT IT Is ͑3x Ϫ 6͒͑x ϩ 1͒ completely factored? Explain. 153. Factor x 2n Ϫ y 2n as completely as possible.