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INTRODUCTION TO ALGEBRA

It is a branch of mathematics in which letters are used for unknown quantities or numbers, arithmetic
operations and rules for manipulating these symbols.

Variables, Constants and Coefficient Powers on Variables Algebraic Expressions

A symbol that represents one or The repeated product of variables The combination of constants
more numbers is called a variable. with itself is written in the form and variables connected by the
E.g., 4x + 1 of their powers or in exponential fundamental mathematical
form. E.g., operations (+, –, ×, and ÷).
• x × x = x 2
The numerical A term without E.g., 4x – 2y + 7
factor of a term that a variable • y × y × y = y
3
contains a variable is called a
2 2
is a coefficient. constant. • p × p × q × q × r = p q r
Factors of Terms Terms

Parts of an algebraic
Expression.
Algebraic Expression 2x – 3xyz E.g., In 3ab + 2bc + ca,
3
Terms 2x 3 –3xyz terms are: 3ab, 2bc, and –ca.

Factors 2 x x x –3 x y z

Types of Algebraic Expressions

Monomials Binomials Trinomials
Expressions that have only Expressions that have only Expressions that have only
one term. E.g., 5x, – 7y, 9, two terms. E.g., x + y, 2x + 3, three terms. E.g., x + 3x + 5,
2
and 2x p – q , and 4 – 5xy y – 6y – 9 and x + x + x
2
2
2
2
2
Polynomials

An algebraic expression containing one or more terms is called a polynomial.
2
2
2
2
2
2
E.g., 2x + 4xy + 4xy + y and 6p – 2p q + 3pq – q
2
Finding the Value of an Algebraic Expression
To evaluate an expression, we substitute the value of the variable in the expression and then simplify
the expression.
E.g., 3x – 7 if x = –1, then 3 × (–1) – 7 = –3 – 7 = –10.

123 Introduction to Algebra