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.
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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!
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.
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Simplifying Multiplication
How to multiply two or more terms. (Two monomials)
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Simplifying Using the Distributive Property
How to use the distributive property to multiply parenthesis. (Multiplying a Monomial and Binomial)
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Simplifying Using the FOIL Method
Using the FOIL Method to multiply two or more parentheses. (Multiplying two Binomials, or two Polynomials)
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Simplifying Exponents of Numbers
Learn what an exponent is, and how to simplify one.
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Simplifying Exponents of Variables
Learn how to simplify a variable inside a parenthesis with an exponent.
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Simplifying Exponents of Polynomials (Parentheses)
Learn how to simplify an exponent of a polynomial, or two or more terms inside a parenthesis.
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Order of Operations
Learn how to use the Order of Operations to simplify expressions containing more than one operation.
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Simplifying Negative Exponents
An introduction to the meaning of negative exponents.
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Simplifying Negative Exponents of Variables
Use fractions to convert negative exponents to positive exponents.
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Simplifying Fractions with Negative Exponents
Simplify negative exponents in fractions by moving parts of a term to the other side of a fraction bar.
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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.
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Greatest Common Factor (GCF)
Find Greatest Common Factors for both numbers and algebraic terms.
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GCF From an Expression
Factor the Greatest Common Factor out of a polynomial.
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Factoring a Difference Between Two Squares
Factor an expression of the form a^{2} – b^{2}.
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Factoring a Trinomial
Factor an expression of the form ax^{2} + bx + c.
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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.
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Equations – Advanced Solving
Solve by Factoring
Solve equations by moving terms to the left side, factoring, and solving several subproblems.
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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.
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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.
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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 3D 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.