 # Algebra Help

Need some algebra help? Or just wanting to review some key concepts in algebra? Here are some lessons to get you started on this important branch of math. With these lessons, algebra will no longer be a mystery reserved for the selected few.

An overview of algebra word problems (includes videos and step by step solutions) covers the common types of word problems in high school and college prep math and the various techniques for solving them.

Free Algebra Worksheets are available to provide practice on some of the following topics, for example solving of equations.

### Introduction

 Basic Algebra An introduction to Algebra Basic Algebra Terms Constants, Variables, Coefficients, Terms, Expressions, Equations, Quadratic Equations Number Properties Commutative property, Associative property, Distributive property
 Algebraic ExpressionsVariables, constants, terms, expressions, and coefficients Writing Algebraic Expressions Translate from words to algebraic expressions Adding and Subtracting Expressions Multiplying and Dividing Expressions Simplifying Expressions Multiplying Expressions or Expanding Expressions FOIL Method used to distribute two binomials

### Techniques to Solve Equations

 Isolate the Variable (Transposition) Combine Like Terms Cross Multiplication Solving Linear Equations Solving Equations by Addition or Subtraction Solving Equations by Division, Multiplication or taking the Reciprocal Solving Equations by Combining Like Terms Solving Equations with Variables on Both Sides Solving Algebra Equations by Distributive Property Solving Muti-Step Equations Solving Equations with Absolute Values Solving for a Variable in a Formula

### Systems of Linear Equations, or Simultaneous Equations

 Solve Systems of Equations by Substitution Solve Systems of Equations by Addition Method (Opposite-Coefficients Method) Solve Systems of Equations Graphically

### Inequalities

 Inequalities and the Number Line Operations on Inequalities Solving Single-Step Inequalities by Addition or Subtraction Solving Single-Step Inequalities by Multiplication Solving Single-Step Inequalities by Division Graphing Linear Inequalities Compound Inequalities Solving Systems of Linear Inequalities / Simultaneous Linear Inequalities Absolute Value Inequalities Solving Quadratic Inequalities

### Factoring and Solving Quadratic Equations

 Factoring Quadratic Equations Finding Common Factors Square of Sum Square of Difference Difference of Two Squares Coefficient of x2 is 1 Coefficient of x2 is greater than 1 Difference of Squares Square of Sum or Perfect Square Trinomials Completing the Square Graphical Solutions of Quadratic Equations How the solutions of a quadratic equation is related to the graph of the quadratic function, how to use the graphical method to solve quadratic equations.

### Factoring Trinomials

 Factoring Trinomials Factoring Trinomials by GCF Factoring Perfect Square Trinomials Factoring Trinomials by Grouping Factoring Trinomials by Trail and Error - Unfoiling Factoring Trinomials with Two Variables

### Polynomials

 Adding and Subtracting Polynomials FOIL method used to multiply two binomials Multiplying Polynomials Dividing Polynomials by Monomials Dividing Polynomials by Long Division Synthetic Division Factoring by Grouping Remainder Theorem Factor Theorem Solving Cubic Equations Binomial Theoerm

### Rational Expressions

 Simplifying Rational Expressions Adding Rational Expressions Subtracting Rational Expressions Multiplying Rational Expressions Dividing Rational Expressions Partial Fraction Decomposition

### Logarithms

 Introduction to Logarithms Solving Logarithmic Functions Common and Natural Logarithms Logarithm Rules or Properties of Logarithms Proof for the Properties of Logarithms Solving Logarithmic Equations Graphs of Logarithmic Functions

### Functions

 Relations and Functions Function Notation Domain and Range of a Function Arithmetic Operations on Functions Composite Functions Functions & Composite Functions Inverse of a Function

### Real Number Videos

 Adding and Subtracting Real Numbers Multiplying and Dividing Real Numbers Properties of Real Numbers Identity Property of 1 and 0 Order of Operations for Real Numbers

### A series of Mathematics Lessons given in videos by Portland Community College - Algebra Review

The vocabulary of algebraic expressions
The geometry of algebraic expressions, Combining like terms
Simplifying Algebraic Expressions using the distributive property
An introduction to equations
Why do we write equations? What is an equation?
What is a solution to an equation? Different types of equations
Introduction to linear equations

Equations that involve simplification, Equations containing fractions.
A general strategy for solving linear equations
Solution Sets: Solutions vs solution sets ? graphing solution sets
Identity equations and inconsistent equations; the empty set; the set of real numbers Solution sets for linear equations
Solutions and solution sets to inequalities; set builder notation
Solving linear inequalities that have only one variable
Solution sets to inequalities, The addition property of inequalities
The positive and negative property of inequalities
The negative multiplication property of inequalities

Modelling and solving word problems using algebra
Word problems with one unknown
Word problems with more than one unknown
An alternative strategy for thinking through the problem

Percents, fractions and decimals
A basic blueprint for percent questions
A bona-fide application involving percents

Mixtures and solutions
The fundamental concept of mixing it up in mixture problems, Examples

Ratio, rates and rational numbers, Proportions
Problem Solving with Proportions
Direct proportions, Inverse or reciprocal proportions
Proportions in geometry

Introduction to perimeter and area
Perimeter, circumference and linear units
Three-dimensional geometry
Introduction to volume and surface area
Volume and surface area formulas

Solutions sets to equations with one variable
Solution sets to linear inequalities with one variable
Solution sets to equations with two variables

Table of values, Application
Slope between two points, Slope of a line
Positive slope, negative slope, zero slope
Determining slope from tables: Computing ?rise over run? given a table of data Determining whether a table of data describes a linear relationship
Generating a table of data from a verbal description

Sign on slope, Magnitude of slope, Parallel lines
Comparing slopes: Perpendicular lines, Vertical lines, Horizontal lines
Summary of slopes
Graphing Linear Equations With Two Variables using intercepts
Three forms of the equation for a line Intercepts
Standard Form, Slope-intercept form
Matters of scale: Slippery slope, Broken scale

Given slope and vertical intercept
Given both intercepts, Applications
Slope-intercept form:
Find the equation of a line given the slope and a point on the line
Applications of linear equations
Point-slope form of a linear equation:
Point-slope form, Finding a linear equation given two points on a line
Finding a linear equation given a graph of a line
Applications of Linear Equations

Applications of Linear Inequalities in two variables
Course Review and Summary: Linear Equations
Linear Modelling

What is a solution to a Systems of Linear Equations in Two Variables?
Solving Systems of Linear Equations in Two Variables by Substitution
When is Substitution the best method?
Special Cases, Three Common Solution Methods

A Word Problem, Applications involving money
Linear Systems based in Geometry
Using Substitution to find new formulas from old

Three important rules of exponents
Two important definitions of exponents
An alternate definition of a polynomial
Examples, Find a strategy that will work for you
One last exponent rule

What is a polynomial? Definitions
Evaluating polynomials
Multiplying monomials, The distributive property, Multiplying binomials
Multivariable Product: Multiplying polynomials by monomials, FOIL
Special products, Products involving polynomials with more than two terms
The geometry of polynomial multiplication:, examples and applications
Perfect square trinomials

Powers of ten and place value
Computations using scientific notation, Astronomical Calculations

What is factoring?
The greatest common factor, Factoring out the greatest common factor
Factoring Binomials of the form x2 + bx + c
Recognizing patterns that emerge from FOIL
Guess and check, Factoring binomials
Factoring Trinomials by grouping
Factoring second-degree trinomial expressions
Factoring multivariable trinomial expressions

Perfect Square Trinomials
Difference of Squares, Sum or difference of cubes
Discuss what went wrong in the following ?factorizations?

The zero-product principle

Simplifying Square Roots Rationalizing the denominator
Solving Quadratic Equations using the square root property
What is the quickest method to solve a quadratic equation?

Working with formulas
Graphs of Parabolas
The axis of symmetry and the vertex

The Graphing Form of Quadratic Equations in Two Variables
Applications involving maxima and minima

Relations, Domain, Range
Definition of a Function, Function Notation
Numerical and Graphical Representation of Functions

Systems of Equations, Exponents and Square Roots
Questions on Systems of Equations, exponents, square roots, scientific notation, quadratics

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 