ALGEBRAIC TERMINOLOGY

BY: MÓNICA ELIZONDO YANN VILLARREAL

OBJECTIVES

• Hello, students! By the end of this section you will be able to:

• Interpret and translate expressions from the common language into symbolic language and viceversa.

• Perform the basis algebraic operations of polynomials.

• Identify the different laws of the exponents to apply them properly in the simplification of expressions and in the performing of multiplication and división of polynomials.

• Transform a number from standard notation to scientific notation and viceversa

• Solve exercises and problems of the world applying the scientific notation

• Overall you will learn algebraic terminology, which will help you through all this course of mathematics!

ALGEBRAIC TERMINOLOGY

• In algebra we use, besides numbers, other symbols like letters of the alphabet that represent magnitudes, quantities or non explicit numeric values. For example we can use a variable like “x” to express the side of an angle which magnitude we don’t know. We will see some examples ahead that will help you to understand.

Common language Symbolic Language

Any number x

The half of a number

The addition of a number to 5

x + 5

The quotient of two numbers

A number increased by 4 x + 4

The consecutive of a x number

x + 1

The double number of x 2x

The double of the consecutive of a number

2(x+1)

The consecutive of the double of a number

2x + 1

The triple of a number added to the double of

other

3x + 2s

EXAMPLE 1

Write in symbolic language each one of the following expressions:

• $67 more expensive than x

• The addition of two numbers is 9

• The area of a square of side b

Answers:

x + 67x + y = 9

DEFINING THE DIFFERENT TERMINOLOGY IN ALGEBRAIC EXPRESSIONS• Now, you will learn some of the basic expressions used in algebraic terminology so that the

communication with other is efficient.

In algebra, the numbers represented by letters are called variables or literals.

The number that is multiplying the variable is

called the coefficient

Example:5xy

5 is the coefficientx and y are the variables

EXPONENTS

Let’s consider the next multiplication: (x)(x)(x)

(x)

This number can be also represented by:

The definition is that the variable “x” is

multiplied 4 times by itself

The x is called the base and the expression is

called power

ALGEBRAIC EXPRESSIONS AND THEIR PROPERTIESTerminology Expression

Any combination of literals and constants that contain the operations of addition, subtraction, multiplication, division, powers and radicals is called: algebraic expression

2ab

x + y

When in an algebraic expression appear only operations of addition, subtraction, product or power, the expression receives the name of: polynomial

An algebraic expression that only contains coefficient and literal part is called: term -5xy

POLYNOMIALS

Taking into consideration the number of terms a polynomial has, it can be classified as the following:

• Monomial: polynomial of only one term

• Binomial: polynomial with two terms

• Trinomial: polynomial with three terms

Polynomial Terms

Monomial X

Binomial

Trinomial

REDUCTION OF LIKE TERMS

LIKE TERMS AND THEIR RULES

The terms that have the same variable are called like terms

In an operation where two or more like terms are substituted by one term is called: reduction of like terms

1. When two or more like terms have the same sign, their coefficients are added and the result of the addition is put next to the corresponding variable.

2. When two or more like terms have contrary signs the numeric coefficients are subtracted. Then the result of the subtraction is put next to the like term.

3. When a polynomials have different signs all the ones with the same terms are added (step 1) and then we go ahead to do step 2

EXAMPLE 2

• Reduce like terms in the following expression:

4x2+ 15x – 17 – 2x2+ 2x+4+13x2-10x- 9

We add and subtract like

terms4x2 – 2x2 + 13x2 15x2

We repeat this step with the

other like terms

Answer15x2+7x-22

Process

REMEMBER!

• If you have any doubt don’t be scared to ask any of the math teachers which will help you as gladly as possible!

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