By Ron Larson, Robert P. Hostetler
This market-leading textual content maintains to supply scholars and teachers with sound, regularly based motives of the mathematical recommendations. Designed for a two-term path, the hot 7th variation keeps the good points that experience made Algebra and Trigonometry an entire answer for either scholars and teachers: attention-grabbing purposes, state-of-the-art layout, and cutting edge expertise mixed with an abundance of rigorously written routines.
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75. 77. 79. 80. 81. 82. 83. 84. 85. 87. 89. 91. 93. 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.
You do not need to memorize these formulas because you can use the Distributive Property to multiply. However, becoming familiar with these formulas will enable you to manipulate the algebra more quickly. Special Products Let u and v be real numbers, variables, or algebraic expressions. 3 Example 5 Polynomials and Special Products 31 Sum and Difference of Same Terms Find the product of 5x ϩ 9 and 5x Ϫ 9. Solution The product of a sum and a difference of the same two terms has no middle term and takes the form ͑u ϩ v͒͑u Ϫ v͒ ϭ u 2 Ϫ v 2.
THINK ABOUT IT When the polynomial Ϫx 3 ϩ3x2 ϩ 2x Ϫ 1 is subtracted from an unknown polynomial, the difference is 5x 2 ϩ 8. If it is possible, find the unknown polynomial. 127. LOGICAL REASONING Verify that ͑x ϩ y͒2 is not equal to x 2 ϩ y 2 by letting x ϭ 3 and y ϭ 4 and evaluating both expressions. Are there any values of x and y for which ͑x ϩ y͒2 ϭ x 2 ϩ y 2 ? Explain. 4 FACTORING POLYNOMIALS What you should learn • Remove common factors from polynomials. • Factor special polynomial forms. • Factor trinomials as the product of two binomials.