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How to Add and Subtract with Powers

To add or subtract with powers, both the variables and the exponents of the variables must be the same. You perform the required operations on the coefficients, leaving the variable and exponent as they are. When adding or subtracting with powers, the terms that combine always have exactly the same variables with exactly the same powers. [more…]


How to Write Numbers in Scientific Notation

Scientific notation is a standard way of writing very large and very small numbers so that they're easier to both compare and use in computations. [more…]

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Graph an Area Where Inequalities Overlap

You can find the solution of a system of inequalities involving a line and a curve (such as a parabola), two curves, or any other such combination.

You do this by graphing the individual equations, determining [more…]


Apply Additive and Multiplicative Identities in Algebra

The numbers zero and one have special roles in algebra — as additive and multiplicative identities, respectively. You use identities in algebra when solving equations and simplifying expressions. [more…]


The Multiplication Property of Zero

The multiplication property of zero is really useful for doing algebra. Of course, you may be thinking that multiplying by zero is no big deal. After all, zero times anything is zero, right? Well, that's [more…]


Simplify Linear Algebraic Equations by Removing Fractions

The problem with fractions in linear algebraic equations is that they aren't particularly easy to deal with. For example, they always require common denominators before you can add or subtract them. [more…]


Isolate an Unknown Variable in an Algebraic Equation

Life isn't always as easy as one-variable equations. Being able to solve an algebra equation for some variable when it contains more than one unknown can be helpful in many situations. [more…]

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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…]

Factoring Special Problems

Binomials, their powers, and their products with selected trinomials occur frequently in algebraic processes. By using the patterns shown here, you save time and reduce the opportunity for errors. [more…]

Formulas for Common Geometric Shapes

Depending on the algebra problem, you'll need to know some geometry. The following represents some of the most common shapes in geometry and their formulas for perimeter, area, volume, surface areas, and [more…]

Order of Operations in Algebra

When creating simpler and more useful expressions, you want to be careful not to change the original value. By applying the order of operations, you maintain that value. [more…]

Rules of Exponents

Exponents are shorthand for repeated multiplication. The rules for performing operations involving exponents allow you to change multiplication and division expressions with the same base to something [more…]

Selected Math Formulas Step by Step

Algebraic formulas make life (and algebra) simpler. You save time by not having to perform more complicated tasks. When using the formulas, use the appropriate rules for simplifying algebraic expressions [more…]

Algebra Workbook For Dummies Cheat Sheet

Formulas, patterns, and procedures used for simplifying expressions and solving equations are basic to algebra. Use the equations, shortcuts, and formulas you find for quick reference. This Cheat Sheet [more…]

How to Convert Square Roots to Exponents

Finding square roots and converting them to exponents is a relatively common operation in algebra. Square roots, which use the radical symbol, are nonbinary operations — operations which involve just one [more…]