A serious student's guide to algebraic expressions
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About the book It focuses on the transformation, simplification, and evaluation of algebraic expressions. This book does not encompass the entirety of elementary algebra, however. For instance, it does not include topics such as equations and inequalities, and it does not involve complex numbers. In short, this book is exclusively devoted to building the core skill of manipulating algebraic expressions, which is foundational for any other mathematical study. It is a comprehensive guide that contains: (1) Detailed explanation of topics (2) Worked examples (3) Abundant exercises of increasing di...
About the book It focuses on the transformation, simplification, and evaluation of algebraic expressions. This book does not encompass the entirety of elementary algebra, however. For instance, it does not include topics such as equations and inequalities, and it does not involve complex numbers. In short, this book is exclusively devoted to building the core skill of manipulating algebraic expressions, which is foundational for any other mathematical study. It is a comprehensive guide that contains: (1) Detailed explanation of topics (2) Worked examples (3) Abundant exercises of increasing difficulty level (4) Solutions to all exercises. It is tailored for dedicated students who are ready to navigate the content diligently, embracing ``productive struggle" with a positive attitude. Motivation There exists a substantial disparity between the content students are taught in secondary schools and the real-world challenges they encounter in colleges, universities, and workplaces. During their time in secondary school, students learn to manipulate only very simple algebraic expressions. The school curriculum does not pay enough attention to developing the necessary depth in this aspect. Yet, as students progress into their post-secondary studies, they are expected to handle much more complex expressions than they used to encounter in their secondary school. Many students of colleges and universities cannot keep up with the amount and speed of what they are taught, simply because they cannot transform algebraic expressions. What makes matters worse is that post-secondary institutions completely ignore this problem: professors do not have time to review algebraic expressions and teach under the assumption that their students are experts in this regard. Reaching the level of mastery expected from students by colleges and universities, or dictated by the realities of modern quantitative occupations, requires special preparation - and this is precisely where this book can offer assistance. Prerequisites The only prerequisites for working through this guide are a strong grasp of arithmetic and an ample supply of pens and paper for completing exercises. No calculator is necessary for any exercise. Topics covered Evaluation of expressions, expressions involving exponents and radicals, distributive rule, collecting like terms, FOIL and expansion equalities, expansion and factoring techniques, polynomials (including long division and composition), expressions involving factorial, sigma and product notations, arithmetic and geometric progressions, general binomial expansion and more. Every chapter has the following structure: Detailed explanation of topics. Examples of worked exercises. Abundant exercises of varying difficulty level. Solutions to all exercises are available in the second half of the book.
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