Algebra

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Algebra

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…]

Algebra

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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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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Basics of Positive and Negative Numbers

Positive and negative numbers are all integers. Integers are whole numbers that are either greater than zero (positive) or less than zero (negative). For every positive integer, there's a negative integer [more…]

How to Use Opposite Operations

When solving an equation in algebra, you will often use an opposite operation such as additive inverse or multiplicative inverse (reciprocal) to work your way toward the answer. You have to undo operations [more…]

How to Subtract Fractions

You can subtract proper fractions that have different denominators — such as thirds and sixths — if you find the common denominator first. The biggest step in subtracting proper fractions is finding the [more…]

How to Compare Numbers by Using Exponents

You can compare number values more easily when you use exponents, because numbers — especially large ones — can be deceiving. To discover the real value of a large number, write it as a number between [more…]

How to Solve Problems Using Exponential Expressions

Using exponential expressions to solve problems that involve repeated actions is the best way to find the answer. Exponential expressions help you figure out problems that do the same thing over and over [more…]

How to Raise Powers of Powers

When raising a power to a power in an exponential expression, you find the new power by multiplying the two powers together. For example, in the following expression, x to the power of 3 is being raised [more…]

Working with Negative Exponents

Negative exponents are a way of writing powers of fractions or decimals without using a fraction or decimal. You use negative exponents as a way to combine expressions with the same base, whether the different [more…]

When to Distribute or Add First in Algebraic Distribution

When performing algebraic distribution, you get the same answer whether you distribute first or add what’s within the parentheses first. Deciding to distribute or add is a judgment call, based on the following [more…]

How to Distribute Negative Signs with Variables

When you use negative signs and multiple variables in algebraic equations, the problems can look scary. Don’t worry, though. All you need to do is distribute the negative sign through, changing the signs [more…]

How to Simplify Negative Exponents with Variables

Distributing with negative exponents means that you'll have fractional answers. A base that has a negative exponent can be changed to a fraction. The base and the exponent become the denominator, but the [more…]

How to Distribute Trinomials

A trinomial, a polynomial with three terms, can be distributed over another expression. Each term in the first factor is distributed separately over the second factor, and then the entire expression is [more…]

Understanding Basic Algebra Vocabulary

Knowing basic algebra vocabulary can help you translate key algebra words into algebra problems. By knowing the definitions of algebra vocabulary in this list, you will be able to construct and solve algebra [more…]

How to Distribute a Polynomial

Distributing a polynomial isn't hard. When distributing a polynomial over any number of other terms, you distribute each term in the first factor over all of the terms in the second factor. When the distribution [more…]

How to Distribute with Fractional Powers or Radicals

Distribution problems with fractional powers or radicals aren't as intimidating as they look. When distributing with fractional powers or radicals, remember that exponents that are fractions work the same [more…]

How to Distribute Binomials

When you distribute in algebra, you multiply each of the terms within the parentheses by another term that is outside the parentheses. So, when you distribute a binomial over several terms, you just apply [more…]

How to Recognize a Perfectly Squared Binomial

Recognizing a perfectly squared binomial can make life easier. When you recognize a perfectly squared binomial, you've identified a shortcut that saves time when distributing binomials over other terms [more…]

Finding the Sum and Difference of the Same Two Terms

When distributing binomials over other terms, knowing how to find the sum and difference of the same two terms is a handy shortcut. The sum of any two terms multiplied by the difference of the same two [more…]

How to Find the Sum of Two Cubes

Spotting a distribution that results in the sum of two cubes is a shortcut to solving distribution problems. To recognize what distribution results in the sum of two cubes, look to see if the distribution [more…]

How to Find the Difference of Two Cubes

An expression that results in the difference between two cubes is usually pretty hard to spot. The difference of two cubes is equal to the difference of their cube roots times a trinomial, which contains [more…]

How to Round Off Decimals and Fractions

You can simplify decimals and fractions by rounding off. To round off a decimal number, you limit the number of decimal places that the number holds. To round off a fraction, you first convert the fraction [more…]

How to Factor Out Numbers

Factoring is the opposite of distributing. When distributing, you multiply a series of terms by a common factor. When factoring, you seek to find what a series of terms have in common and then take it [more…]

How to Factor Out Variables

You can factor out variables from the terms in an expression. You factor out variables the same way as you do numbers except that when you factor out powers of a variable, the [more…]

Factoring Binomials

If a binomial expression can be factored at all, it must be factored in one of four ways. To decide which way you will use, you first look at the addition or subtraction sign that always separates the [more…]

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…]

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