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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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How to Distribute Positive and Negative Numbers
When performing distribution, be aware of the sign being distributed and how that sign affects each term. Distributing a positive sign makes no difference in the signs of the terms — the signs stay the [more…]
Combining Square Roots
Square roots, which use the radical symbol, are nonbinary operations — operations which involve just one number — that ask you, “What number times itself gives you this number under the radical?” Finding [more…]
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…]
