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# Algebra Lessons Index

If you have little or no algebra background, you may read the lessons in the order listed below.  If you have some algebra background, you can usually skip to any topic that you need to learn or review.

## Algebra Basics

Equation Basics
The equation and its relationship with a balance.
 Sample Problem 2x + 7 = x + 18 Solution x = 11

Proportion Basics
How to solve basic proportions.
Sample Problem
 12 = 4 3 x
Solution   x = 1

Word Problem Basics
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

## 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

Multiplication
How to multiply two or more terms. (Two monomials)
 Sample Problem 2x * 7y Solution 14xy

Distributive Property
How to use the distributive property to multiply parenthesis. (Multiplying a Monomial and Binomial)
 Sample Problem 5u * (3 + u) Solution 15u + 5u2

FOIL Method
Using the FOIL Method to multiply two or more parenthesis. (Multiplying two Binomials, or two Polynomials)
 Sample Problem (4x + 5)(7x + 3) Solution 28x2 + 47x + 15

Exponents of Numbers
Learn what an exponent is, and how to simplify one.
 Sample Problem 24 Solution 16

Exponents of Variables
Learn how to simplify a variable inside a parenthesis with an exponent.
 Sample Problem (x2y)3 Solution x6y3

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

Negative Exponents
An introduction to the meaning of negative exponents.
 Sample Problem 5-2 Solution 0.04

Negative Exponents of Variables
Use fractions to convert negative exponents to positive exponents.

Negative Exponents in Fractions
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.

## 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 Factors (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)

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)

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

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)