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Quadratic Equations
How to Use FOIL to Distribute Two Binomials (Video)
In algebra, variables are placeholder letters (capitalized and lowercase) that represent the unknown, or what you're solving for. This video shows you what variables can look like and what they mean. Understanding variables help make algebra easier for you. [more…]
Quadratic Equations
How to Use UnFOIL to Factor Quadratic Equations (Video)
Using the unFOIL method to factor quadratic equations into two binomials requires many steps. Prime factorization and order of decreasing powers are two parts of the unFOIL method, which helps you solve for quadratic equations. Remember that FOIL stands for first, outer, inner, and last. [more…]
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Algebra Basics
How to Use the Order of Operations
Follow the order of operations with each algebra problem you solve. The order of operations in algebra is important if you want to find the correct answer. You first work through any grouping symbols, [more…]
Quadratics in Algebra
Standard Equations of Algebraic Conics
Conics are curved algebraic forms that come from slicing a cone with a plane. Use these equations to graph algebraic conics, such as circles, ellipses, parabolas, and hyperbolas: [more…]
Linear Equations in Algebra
Cramer’s Rule for Linear Algebra
Named for Gabriel Cramer, Cramer’s Rule provides a solution for a system of two linear algebraic equations in terms of determinants — the numbers associated with a specific, square matrix. [more…]
Counting Techniques
Algebraic Permutations and Combinations
In algebra, you use permutations to count the number of subsets of a larger set. Use permutations when order is necessary. With combinations, you can count the number of subsets when order doesn't matter [more…]
Algebra Basics
Eight Basic Algebraic Curves
Algebra is all about graphing relationships, and the curve is one of the most basic shapes used. Here's a look at eight of the most frequently used graphs. [more…]
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Solving Absolute-Value Equations
A linear absolute value equation is an equation that takes the form |ax + b| = c. Taking the equation at face value, you don’t know if you should change what’s in between the absolute value bars to its [more…]
How to Solve Linear Equations with Division
A basic method for solving linear equations is to divide each side of the equation by the same number. Many formulas and equations include a coefficient, or multiplier, with the variable. To get rid of [more…]
How to Solve Linear Equations with Multiplication
To solve linear equations with multiplication, you first determine that division is being used in the linear equation. Multiplication is the inverse (opposite) operation of division, so you can use multiplication [more…]
How to Identify a Quadratic Expression
You can identify a quadratic expression (or second-degree expression) because it's an expression that has a variable that's squared and no variables with powers higher than 2 in any of the terms. [more…]
How to Solve Linear Equations with Both Multiplication and Division
Often, you need to use both multiplication and division to solve a linear equation. When a linear equation uses both multiplication and division, you solve by using the inverse operation of each. So, if [more…]
How to Factor an Expression Taking out the Greatest Common Factor
You can factor a quadratic expression to make it easier to work with. Some quadratic expressions can be made better by finding a greatest common factor [more…]
Applying the FOIL Method to Binomials
When you multiply two binomials, you can use the FOIL method. The letters in FOIL refer to two terms — one from each of two binomials — multiplied together in a certain order: [more…]
How to Multiply Binomials Using the FOIL Method
The FOIL method lets you multiply two binomials in a particular order. You don't have to multiply binomials by following the FOIL order, but it does make the process easier. The letters in FOIL refer to [more…]
How to Factor a Trinomial by UnFOILing
UnFOILing is a method for factoring a trinomial into two binomials. When you multiply two binomials together, you use the FOIL method, multiplying the [more…]
How to Factor Expressions More Than Once
Sometimes you factor expressions more than once — and with different factoring techniques. To determine if an expression needs to be factored more than once, just take another look at the expression after [more…]
How to Solve Linear Equations with Reciprocals
You can use the reciprocal of the number that you’re trying to “get rid of” if a fraction is multiplying the variable. You solve linear equations with reciprocals when you see a fraction — it's easier [more…]
How to Unevenly Group Four Terms for Factoring
Sometimes in factoring, four terms can be separated into uneven groupings with three terms in one group and one term in the other. Unevenly grouping four terms for factoring can be applied to expressions [more…]
How to Factor the Sum of Two Perfect Cubes
The rule for factoring the sum of two perfect cubes is almost the same as the rule for factoring the difference between perfect cubes. You just have to change two little signs to make it work. The sum [more…]
How to Factor the Difference of Two Perfect Squares
If two terms in a binomial are perfect squares separated by subtraction, then you can factor them. To factor the difference of two perfect squares, remember this rule: if subtraction separates two squared [more…]
How to Add Fractions
Adding fractions is easy if the denominators are the same, but adding fractions with different denominators requires care. If you set up an algebraic equation to add fractions with different denominators [more…]
How to Factor the Difference of Two Perfect Cubes
To factor the difference of two perfect cubes, remember this rule: the difference of two perfect cubes equals the difference of their cube roots multiplied by the sum of their squares and the product of [more…]
How to Group Six Terms for Factoring
You can group terms for factoring in expressions where the terms don't share a common factor or common variable. When grouping six terms for factoring, there’s the chance that the groups can be two groups [more…]
Order of Operations in Algebra
Solve algebra problems correctly by following the order of operations. When performing more than one operation on an algebraic expression, work out the operations and signs in the following order: [more…]
Algebra Formulas Worth Memorizing
Some formulas occur frequently when you're doing algebraic manipulations and working through mathematical applications. You'll find ways to use these algebra formulas even when you're doing something other [more…]
Algebra's Rules of Divisibility
In algebra, knowing the rules of divisibility can help you solve faster. When factoring algebraic expressions to solve equations, you need to be able to pull out the greatest factor. You also need common [more…]
Algebra I For Dummies Cheat Sheet
Algebra problems are easier to solve when you know the rules and formulas. Memorizing key algebra formulas will speed up your work, too. And if you know the rules of divisibility and the order of operations [more…]
Mathematical Order of Operations
The rules for deciding the order to evaluate arithmetic expressions, no matter how complex, are called the order of operations. The complete order of operations in math are: [more…]
Mathematical Inequalities
When two numbers are different in value, a variety of symbols are used to turn them into an inequality. The four most common inequalities in arithmetic are: [more…]
Mathematical Place Value
Our number system (Hindu-Arabic) has ten familiar digits, 0 to 9. Numbers higher than 9 are made using place value, which assigns a digit a greater or lesser value depending on where it shows up in a number [more…]
Understanding Absolute Value and Negation
The positive value of a number is its absolute value. It tells you the distance of a number from zero on the number line. Placing bars (| |) around a number or expression gives you its absolute value: [more…]
