Algebra Tutorials!
   
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Exponential Decay
Negative Exponents
Multiplying and Dividing Fractions 4
Evaluating Expressions Involving Fractions
The Cartesian Coordinate System
Adding and Subtracting Fractions with Like Denominators
Solving Absolute Value Inequalities
Multiplying Special Polynomials
FOIL Method
Inequalities
Solving Systems of Equations by Graphing
Graphing Compound Inequalities
Solving Quadratic Equations by Completing the Square
Addition Property of Equality
Square Roots
Adding and Subtracting Fractions
The Distance Formula
Graphing Logarithmic Functions
Fractions
Dividing Mixed Numbers
Evaluating Polynomials
Power of a Product Property of Exponents
Terminology of Algebraic Expressions
Adding and Subtracting Rational Expressions with Identical Denominators
Solving Exponential Equations
Factoring The Difference of 2 Squares
Changing Fractions to Decimals
Solving Linear Equations
Using Patterns to Multiply Two Binomials
Completing the Square
Roots of Complex Numbers
Methods for Solving Quadratic Equations
Conics in Standard Form
Solving Quadratic Equations by Using the Quadratic Formula
Simplifying Fractions 2
Exponential Notation
Exponential Growth
The Cartesian Plane
Graphing Linear Functions
The Slope of a Line
Finding Cube Roots of Large Numbers
Rotating Axes
Common Mistakes With Percents
Solving an Equation That Contains a Square Root
Rational Equations
Properties of Common Logs
Composition of Functions
Using Percent Equations
Solving Inequalities
Properties of Exponents
Graphing Quadratic Functions
Factoring a Polynomial by Finding the GCF
The Rectangular Coordinate System
Adding and Subtracting Fractions
Multiplying and Dividing Rational Expressions
Improper Fractions and Mixed Numbers
Properties of Exponents
Complex Solutions of Quadratic Equations
Solving Nonlinear Equations by Factoring
Solving Quadratic Equations by Factoring
Least Common Multiples
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Solving Exponential Equations
Solving Linear Equations
Multiplication Property of Equality
Multiplying Mixed Numbers
Multiplying Fractions
Reducing a Rational Expression to Lowest Terms
Literal Numbers
Factoring Trinomials
Logarithmic Functions
Adding Fractions with Unlike Denominators
Simplifying Square Roots
Adding Fractions
Equations Quadratic in Form
Dividing Rational Expressions
Slopes of Parallel Lines
Simplifying Cube Roots That Contain Variables
Functions and Graphs
Complex Numbers
Multiplying and Dividing Fractions 1
Composition of Functions
Intercepts of a Line
Powers
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Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
Exponents and Polynomials
Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
Solving Quadratic Equations
Theorem of Pythagoras
Equations 1
Subtracting Fractions
Solving Quadratic Equations by Graphing
Evaluating Polynomials
Slope
Angles and Degree Measure
   
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Terminology of Algebraic Expressions

In this note we give brief descriptions and illustrations of some names of things encountered in algebra.

An algebraic expression is a sequence of numbers and literal symbols together with arithmetic operation symbols and perhaps pairs of brackets. When the literal symbols are replaced by actual numbers, it should be possible to reduce the resulting numerical expression to a single numerical value.

Examples of algebraic expressions are:

  • 3x + 5y = 7
  • 6(x - 5) 2 + 24x
  • 6x 3 + 5x 2 - 8x + 7
  • (3x 2 + 7x - 1) 4

Algebraic expressions consist of one or more terms. The terms of the expression are the parts of the expression which are separated by ‘+’ or ‘-‘ signs.

Thus, the expression:

 

  • 3x + 5y = 7
has 3 terms
  • 6(x - 5) 2 + 24x
has 2 terms
has 1 term
  • 6x 3 + 5x 2 - 8x + 7
has 4 terms
  • (3x 2 + 7x - 1) 4
has 1 term

 

Terms can be products of two or more factors. A product results when two or more quantities are multiplied together. The quantities being multiplied together to form a product are called its factors. Thus

  • ‘3x’ is the product of two factors, ‘3’ and ‘x’; or ‘3’ and ‘x’ are the factors of the product ‘3x’
  • ‘6x 2y’ is the product of three factors: ‘6’, ‘x 2’, and ‘y’

Of course, ‘x 2’ could itself be regarded as the product of two factors: ‘x’ and ’x’. In that case, 6x 2y becomes the product of four factors.

Often a term is a product of a constant or number and a part which is a literal symbol or a product or two or more literal symbols. The numerical factor is often referred to as the coefficient or numerical coefficient of the term. Thus

  • the term ‘3x’ has the numerical coefficient ‘3’
  • the term ‘6x 2 y’ has the numerical coefficient ‘6’,

etc.

The word coefficient is also used more generally to refer to a factor or group of factors in a term. Thus, for example, in the term 6x 2 y,

‘6x 2 ’ is the coefficient of ‘y’

and

‘y’ is the coefficient of ‘6x 2

Terms which have identical symbolic parts are said to be like terms. Logically, two terms with different symbolic parts would be called unlike terms. So

  • 3x 2 y and 7x 2 y are like terms (the symbolic part in both cases is ‘x 2 y’)

but

  • 3x 2 y and 7xy 2 are unlike terms, because the symbolic part of the first one is x 2 y, which is different from xy 2 , the symbolic part of the second one.

There are specific names for expressions which indicate how many terms they contain:

monomials are expressions with just one term

for example: 5, 6x 2y, 3x, 7xyz, etc. are monomials

binomials are expressions with two terms:

for example: x + y, 3x 2 – 4y, 5 + 2x, etc., are binomials

trinomials are expressions with 3 terms

for example

5x 2 + 2xy -3y 2 is a trinomial

is a trinomial

multinomials are expressions with several terms

polynomials are expressions with two or more terms in which the symbolic part of each term is a power of a single symbol (the same one in all terms). The degree of a polynomial is the highest power that it contains.

for example:

3x 2 + 2x + 5 is a polynomial of degree 2 (or, a polynomial of the second degree)

5x 7 + 3x 4 + 9x 3 - 7x 2 + 2 is a polynomial of degree 7.

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