A Serious Student's Guide to Algebraic Expressions

THIS BOOK:

• Focuses on the transformation, simplification, and evaluation of algebraic expressions. This book does not include topics such as equations and inequalities, and it does not involve complex numbers.
• Is a comprehensive guide that contains: (1) Detailed explanation of topics (2) Worked examples (3) Abundant exercises of varying difficulty level (4) Solutions to all exercises.
• Is tailored for dedicated students who are ready to navigate the content diligently, embracing "productive struggle" with a positive attitude.

The book is appropriate not only for students starting their elementary algebra journey but also for those who have previously completed an elementary algebra course and are aiming to refine and amplify their proficiency with algebraic expressions. Particularly, students preparing for post-secondary education will discover this book to be especially beneficial.

This book offers straightforward style of exposition, with carefully crafted exercises that gradually become more challenging.
At some point exercises become complex, but there are no puzzles or unnecessarily difficult exercises. The quantity of exercises has been chosen to strike the ideal balance – not excessive, not lacking – ensuring the essential practice needed to attain the necessary level of knowledge and automaticity. All exercises have full solutions. The level of this book is precisely aligned with the implicit expectations established by post-secondary institutions for incoming students.

YOUR JOURNEY

Chapter 1: You will begin by learning how to evaluate expressions of varying complexities. Here, no prior knowledge of formulas or techniques for transforming expressions will be required. Your arithmetic skills will be put to use and reinforced.

Chapter 2: You will delve into working with expressions that involve both whole and fractional exponents. This chapter will also introduce you to radicals. By the end of the chapter, you'll confidently handle exponent operations of varying degrees of difficulty.

Chapter 3: The primary techniques for dealing with algebraic expressions, such as using the distributive property and collecting like terms, will be mastered here. Due to their paramount importance, you will engage in extensive practice to firmly grasp these techniques. In this chapter, you will also learn how to work with addition and subtraction of algebraic fractions.

Chapter 4: You will learn how to use crucial expansion equalities. These equalities play a pivotal role in expression manipulation, and you will gain extensive practice in applying them. You will engage with various techniques for expansion and factoring of algebraic expressions. By this chapter's conclusion, you will have become an expert in simplifying algebraic expressions of diverse complexities.

Chapter 5: This chapter focuses on the manipulation of polynomials. You will acquire proficiency in factoring and dividing polynomials, will learn about polynomial composition, and will gain insight into interesting concepts such as non-commutativity and one-sided distributivity.

Chapter 6: Expressions involving factorial, summation (sigma), and product notations will be your focus. These types of expressions are ubiquitous in almost all quantitative fields. As you engage with the exercises in this chapter, you will discover concepts such as arithmetic and geometric progressions, arithmetic and geometric means, variance and standard deviation, Euclidean distance, permutations and combinations, and the binomial theorem.

PREREQUISITES

To use of this book, two prerequisites are essential: (1) A solid grounding in arithmetic and (2) An ample supply of paper and pens, as you will be working through a multitude of exercises. You won't require anything else, not even a calculator.