Understanding Algebra

(updated 16 March 2023)

Algebra is a branch of mathematics that uses letters of the alphabet to represent objects, numbers or even groups of numbers or expressions. In many cases, algebra uses shorthand mathematical notation to simplify complex or very large terms. A major goal in algebra is to solve equations.

I’ve found that knowing about Algebra has been very useful. Understanding algebraic methods is important in science, computing and other math courses. Algebra is used in so many fields that the subject can even help in your career.

The purpose of these lessons is to help you gain understanding the basics of Algebra, such that you do well in school and become a champion in the subject.

Algebra Contents

Basics Terminolgy Properties Exponents and roots Working with expressions Solving equations Quadratic equations

Resources Survey results

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Basics

What is Algebra?

Purpose of Algebra is to Solve Equations

Terminolgy

Terminology Used in Algebra

Variables and Constants in Algebra

Algebraic Operations and Symbols

Algebraic Expressions

Properties

Product of Two Negative Numbers is Positive

Properties or Laws of Addition and Multiplication

Algebra of Objects

Imaginary Numbers

Working with expressions

Combining Like Terms in an Expression

Multiplying Binomial Expressions

Exponents and roots

Exponents

Exponent Rules

Multiplication with Exponents

Division with Exponents

Exponents to the Power of 10

Square Roots

Newton’s Square Root Approximation

Solving equations

Linear Equations

Solving a Linear Equation with One Variable

Quadratic equations

Quadratic Equations

Solving Quadratic Equations by Factoring

Completing the Square Method

Using the Quadratic Equation Formula

Derivation of Quadratic Formula

Resources

Algebra Resources

Graded Tests on Algebra

Arithmetic

Author’s Credentials

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Survey results

See results of survey questions