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Algebra Help Lessons List


Below is a list of all our algebra lessons. Still need help after reading through these lessons? At Wyzant, connect with algebra tutors and math tutors nearby. Prefer to meet online? Find online algebra tutors or online math tutors in a couple of clicks.

Algebra Basics

Equation Basics

The first lesson is about the equation and its relationship with a balance. You'll learn a variety of symbols used in equations and how to think of a balance whenever you solve equations.

Associative Property

Here you'll learn about the associative property, which becomes important because it allows the mathematician, you, to add or multiply numbers with ease.

Proportions

This lesson teaches you how to solve basic proportions, which are a special form of an algebra equation. They're used to compare two ratios or make equivalent fractions.

Word Problems

This lesson introduces methods for solving integer word problems through equations.

Sample Problem   What are two consecutive even integers that have a sum of 26?
Solution   12 and 14

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!


Simplifying

Simplifying Intro

An introduction to simplifying concepts.

Simplifying Multiple Signs

The most basic way to simplify an expression or equation - removing multiple negative signs.

Combining Like Terms

Compacting equations and expressions by combining like terms.

Sample Problem   2x + 7x + 4y
Solution   9x + 4y

Simplifying Multiplication

How to multiply two or more terms. (Two monomials)

Sample Problem   2x * 7y
Solution   14xy

Simplifying Using the Distributive Property

How to use the distributive property to multiply parenthesis. (Multiplying a Monomial and Binomial)

Sample Problem   5u * (3 + u)
Solution   15u + 5u2

Simplifying Using the FOIL Method

Using the FOIL Method to multiply two or more parentheses. (Multiplying two Binomials, or two Polynomials)

Sample Problem   (4x + 5)(7x + 3)
Solution   28x2 + 47x + 15

Simplifying Exponents of Numbers

Learn what an exponent is, and how to simplify one.

Sample Problem   24
Solution   16

Simplifying Exponents of Variables

Learn how to simplify a variable inside a parenthesis with an exponent.

Sample Problem   (x2y)3
Solution   x6y3

Simplifying Exponents of Polynomials (Parentheses)

Learn how to simplify an exponent of a polynomial, or two or more terms inside a parenthesis.

Sample Problem   (x + y)2
Solution   x2 + 2xy + y2

Order of Operations

Learn how to use the Order of Operations to simplify expressions containing more than one operation.

Sample Problem   2 + (3 - 1) * 32
Solution   20

Simplifying Negative Exponents

An introduction to the meaning of negative exponents.

Sample Problem   5-2
Solution   0.04

Simplifying Negative Exponents of Variables

Use fractions to convert negative exponents to positive exponents.

Sample Problem   5-2
Solution   0.04

Simplifying Fractions with Negative Exponents

Simplify negative exponents in fractions by moving parts of a term to the other side of a fraction bar.

Sample Problem   a2b-2 / b
Solution   a2 / b3

Substitution

Substitution Introduction

An introduction to substituting variables in an expression with numbers or other expressions.


Graphs and Graphing

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.


Factoring

Factoring Intro

Explains the basic principles behind factoring.

Factoring Numbers

Factoring numbers, a skill needed for next lessons.

Sample Problem   Find all factors of 18
Solution   1, 2, 3, 6, 9, 18

Greatest Common Factor (GCF)

Find Greatest Common Factors for both numbers and algebraic terms.

Sample Problem   Find the GCF of 14x and 21x2
Solution   7x

GCF From an Expression

Factor the Greatest Common Factor out of a polynomial.

Sample Problem   Factor the GCF from 3x3 + 27x2 + 9x
Solution   3x(x2 + 9x + 3)

Factoring a Difference Between Two Squares

Factor an expression of the form a2 - b2.

Sample Problem   Factor x2 - 4
Solution   (x + 2)(x - 2)

Factoring a Trinomial

Factor an expression of the form ax2 + bx + c.

Sample Problem   Factor 3x2 + 2x - 8
Solution   (x + 2)(3x - 4)

Factoring Completely

Combine the methods of factoring a GCF, Difference Between Two Squares, and Trinomial to determine the most factored form of more complex expressions.

Sample Problem   12x4 - 3x2 - 54
Solution   3(2x + 3)(2x - 3)(x2 + 2)

Equations - Advanced Solving

Solve by Factoring

Solve equations by moving terms to the left side, factoring, and solving several subproblems.

Sample Problem   x2 + 3x = 8x - 6
Solution   x = 2, 3

The Quadratic Equation

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 is an introduction to the quadratic equation. How they are formed, how they are graphed, and a brief look at how they are solved.

Completing the Square

Solve equations which cannot be factored by Completing the Square.

Sample Problem   10x2 + 22x + 12.1 = 0
Solution   x = -1.1 (double root)

Solve by Using the Quadratic Formula

This lesson is a deeper look into the quadratic formula. Solve second degree equations, without factoring or completing the square, by using the quadratic formula.

Sample Problem   x2 + x + -3.75 = 0
Solution   x = -2.5, 1.5

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.

Factor Theorem

The Factor Theorem is an algebraic topic that involves finding the roots (or zeroes) of a polynomial function.

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.

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.

Square Roots and Radicals

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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