By T. T. Moh

This current booklet comes from the 1st a part of the lecture notes the writer used for first-year graduate algebra path on the college of Minnesota, Purdue collage and Peking collage. the purpose of this ebook is not just to provide the scholar easy access to the fundamental wisdom of algebra, both for destiny development within the box of algebra, or for normal heritage info, but additionally to teach that algebra is really a grasp key or "skeleton key" to many mathematical difficulties. the writer needs to offer this publication as an try and re-establish the contacts among algebra and different branches of arithmetic and sciences. Many examples and workouts are integrated to demonstrate the facility of intuitive methods to algebra.

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46 ͑Ϫ4͒6 2. Ϫ47 ͑Ϫ4͒7 3. ͙16 is a positive number. 4. 3 ϩ 5 и 6 3 ϩ ͑5 и 6͒ 5. ͑Ϫ2͒ is a negative number. 6. ͑Ϫ2͒8 is a positive number. 7. The product of 8 positive factors and 8 negative factors is positive. 8. The product of 3 positive factors and 3 negative factors is positive. 7 9. In the exponential expression Ϫ35, Ϫ3 is the base. 11. Evaluate each exponential expression. MathXL Digital Video Tutor CD 1/Videotape 1 2 (a) 8 (c) ͑Ϫ8͒2 (b) Ϫ8 (d) Ϫ͑Ϫ8͒2 2 10. ͙a is positive for all positive numbers a.

The distributive property can also be written ab ϩ ac a͑b ϩ c͒ ba ϩ ca ͑b ϩ c͒a. and It can be extended to more than two numbers as well. a͑b ϩ c ϩ d͒ ab ϩ ac ϩ ad This property is important because it provides a way to rewrite a product a͑b ϩ c͒ as a sum ab ϩ ac, or a sum as a product. ” EXAMPLE 1 Using the Distributive Property Use the distributive property to rewrite each expression. (a) 3͑x ϩ y͒ Use the first form of the property to rewrite this product as a sum. 3͑x ϩ y͒ 3x ϩ 3y (b) Ϫ2͑5 ϩ k͒ Ϫ2͑5͒ ϩ ͑Ϫ2͒͑k͒ Ϫ10 Ϫ 2k (c) 4x ϩ 8x Use the second form of the property to rewrite this sum as a product.

An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 4 (b) y ϩ y 1y ϩ 1y ͑1 ϩ 1͒y 2y Properties of Real Numbers 35 Identity property Distributive property Add inside parentheses. (c) Ϫ͑m Ϫ 5n͒ Ϫ1͑m Ϫ 5n͒ Ϫ1͑m͒ ϩ ͑Ϫ1͒͑Ϫ5n͒ Ϫm ϩ 5n Identity property Distributive property Multiply. Now Try Exercises 21 and 23. Expressions such as 12m and 5n from Example 2 are examples of terms. A term is a number or the product of a number and one or more variables. Terms with exactly the same variables raised to exactly the same powers are called like terms.