Algebra and Algebraic Identities: 4000 Problems with Solutions that show the power of Algebra to aid Arithmetic Computation

Algebra is Very Useful

Many students who encounter algebra for the first time when they enter middle school think that it is only about letters and operations and identities and factors and equations.

They are partly right. Elementary and intermediate algebra are definitely about all those things, but their applications in other fields – physics, economics, biology, business modeling, and so on – are vast, and growing rapidly.

This book focuses on the application of elementary algebraic identities to simplify arithmetic and numerical calculations.
In the age of the calculator and of calculator apps, tedious computations done by hand are almost a thing of the past – but not entirely. As part of the steps required to solve a long problem in mathematics or in allied fields, long numerical calculations are often encountered. It is tedious to pull out the calculator every single time; indeed, some tests do not allow the usage of calculators, even in this day and age.

In such situations, it is very useful to be able to use algebraic identities to simplify complex computations. And who can forget the fact that you look like a genius when you reduce what looks like a difficult task even for a calculator, to something you can do in your head?

This book focuses on the three basic square identities that students spend the first few months of an introductory algebra course mastering. As you go through the theory, through the solved examples, through the Challenge Section, and through the detailed drills, you will find that it is flexible, and that the difficulty level rises slowly. You will be able to level up till your expertise in the subject matches that which you require in your chosen field of study; you can spend ten hours or a thousand hours on the exercises in this book, according to your requirement.

Future books in this series will explore the applications of other identities from intermediate algebra, including the cubic identities.

I am confident that the tools you learn in this book will stand you in good stead throughout your education, and throughout your career.

Best of luck!