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This section contains explanations of key algebra topics with interactive examples and quizzes. The topics are arranged in a cumulative way starting with some basic ideas and building up to more complicated aspects of algebra.

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Properties of Algebra

You should be familiar with these basic algebraic properties as you start your lessons in algebra. These properties apply to all real numbers and include the cumulative property, the commutative property, and more. Before you try to solve algebra problems, learn these!

The Order of Operations

Algebra equations can look complicated to new students. Learn how to decipher all those symbols with this primer on the Order of Operations. How do you evaluate an equation containing parentheses and exponents? Read this lesson to find out.

The Distributive Property

The distributive property is a helpful algebra property that makes multiplying numbers easier. This lesson will explain how to multiply numbers inside parentheses. You’ll also learn tips for quickly multiplying large numbers.

Factorization

Factorization is the process of breaking down an expression into products called factors. This concept will help you simplify large, complicated numbers into something you can actually work with. This lesson covers the different methods of factorization, such as factorization by grouping or factorization by taking the difference of two squares.

Solving Equations

Once you’re familiar with the order of operations and different algebraic properties, you can finally get down to the business of solving equations. This lesson describes the terms "expression" and "equation" and walks you through solving a one variable equation.

Graphing Linear Equations

Graphs provide a visual representation of the relationship between two variables. In this lesson, learn how to graph and solve two variable equations, and become comfortable with coordinate planes, ordered pairs, and more.

Inequalities

Inequalities, such as the “greater than” ( > ) and “less than” ( < ) relationships, can be visualized and solved just like normal equations. This lesson introduces inequalities and explains how to solve inequalities with variables, and how to show inequalities on a number line.

Graphing Linear Inequalities

After solving basic inequalities, you’re ready to move onto solving and graphing two variable inequalities. In this lesson, you will learn how to solve a linear inequality, represent a linear inequality on a graph, and (most importantly!) check your work to make sure you’ve mastered the concept.

Slope of a Line

The slope of a line is an essential concept in many areas of mathematics, algebra included. How do you calculate slope? What are some common mistakes to avoid? Learn all about “rise over run” in this lesson.

Functions

Functions express the relationship between two variables. OK, now what does that mean? Read on for a simple definition and explanation of functions. Confused about the vertical line test? Not sure what the difference is between an even function and an odd function? You’ll find the answers here.

FOIL Method

First Outside Inside Last. The FOIL method defines how two binomials are multiplied. Algebra students need to understand what FOIL stands for and means. Read on for an explanation and plenty of examples.

Polynomials

A polynomial is an expression of finite length, including variables with positive whole number exponents. This lesson describes polynomials, polynomial roots, and includes an introduction to quadratic polynomials.

Complex Numbers

What happens when you combine real numbers and imaginary numbers? You get a complex number. Learn how to solve equations involving complex numbers in this lesson. Need more information on imaginary numbers? This lesson covers that too.

When you have a polynomial function of degree two, you have a quadratic function. When a quadratic function is equated to zero, you have what is called a quadratic equation. This lesson covers quadratic equations in depth. How are they formed, how do you graph them, and how do you solve them?

If you want to find the roots of quadratic equations, you’re going to need the quadratic formula. In this lesson, you will learn about the quadratic formula, its derivations, and its discriminant.

The Remainder Theorem

The remainder theorem can be used to quickly factorize a polynomial of any degree. You can tackle difficult problems with this helpful theorem. Read this lesson to learn where the remainder theorem comes from and how to use it, with detailed examples.

Exponents

Also known as “powers of” numbers, exponents are operators used to multiply a number by itself a certain number of times. Exponents can be positive numbers, negative numbers, or many more special numbers. Learn about the different kinds of exponents and their properties in this lesson.

Logarithms

You can think of a logarithm as the opposite of an exponent: It’s an operation to undo an exponent. This lesson defines logarithms and takes you through several example problems.

A square root is a number which, when multiplied by itself, gives a square. Did you know every square has two square roots? How do you define a cube root? This lesson answers these questions and explains many concepts related to square roots and radicals.

Rationalization

Rationalization is the process of making a fraction rational. When do you need to make a fraction rational? When it’s irrational, of course. Read this lesson for examples of rationalization and a practice quiz.

Rational Expressions

Also known as rational functions, a rational expression includes polynomials in its numerator and denominator. Can you find the domain of a rational expression? Do you know how to simplify a rational expression? This lesson will walk you through the process.

Conic Sections

Conic sections are formed by slicing a 3-D circular cone. The four kinds of conic sections are circles, ellipses, parabolas, and hyperbolas. In this lesson, learn how to represent all four conic sections with equations and graphs.

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