Lesson 1
Algebraic Expressions
Terms
To familiarize ourselves with algebra we
must know some terms associated with it.
Literals:
The letters which are used to represent
numbers are called literal numbers or
literals. A literal is also called a variable
Term: A numerical constant or the product
(or quotient) of a numerical constant and
one or more variables.
Example: 5x, 3xy, -4ab
Algebraic Expression:
It is a combination of one or more terms.
The terms in an algebraic expression are
separated by either + or - signs.
Example: 5pq, 7ab + 6, 6x2 - 4x - 9
Types
Algebraic expressions can be classified based
on the number of terms they contain. Before we
get into the classification of algebraic
expressions let us know some basic points.
 In a term like 4pq, the numerical constant 4 is
called the numerical coefficient.
 A number without any variable is called a
constant term.
Types of algebraic expressions:
Monomial: An expression with one term
Example: -6ab
Types of algebraic expressions:
Binomial: An expression with two terms.
Example: 9xy + 4x2
Types of algebraic expressions:
Trinomial: An expression with three terms
Example: -2p, +3q, 15pq
Property
While dealing with algebraic expressions
and their simplification it is important to
know about a special property called the
distributive property.
Distributive property
Let us say we have an algebraic expression of
the type, 25x + 35y, we observe that the terms of
the given expressions have their coefficients 25
and 35 which are multiples of 5.
We can say that they have a common factor that
is 5. Hence we can simplify it as 25x + 35y =
5(5x + 7y)
Distributive property
Let us see another case, 32xy - 8x2y2 here
we observe that not only the numerical
coefficients have a common factor 8 but
also the literal factors are common
Hence, 32xy - 8x2y2 = 8xy(4 - xy)
Distributive property
Hence we can generalize these
statements and frame a general rule
known as the distributive property which is
as follows,
ax + ay = a(x + y)
Substitution
Introduction
Generally, we see questions of the type
'evaluate' that is finding the value of an
expression for a certain assigned
numerical value of the variable
Substitution
 An important technique used in algebra is
substitution, the word substitute means replacing
a quantity with another.
 Substitution is a method which is employed to
evaluate an algebraic expression or express it in
terms of other variables.
 So, if two values are equal, they can be
substituted for each other.
Algebraic Expressions II
We are thorough with substitution
method now. Let us move on to
simplification of algebraic expressions.
Algebraic Expressions II
Like Term
All the four basic operations namely
addition, subtraction, multiplication and
division can be performed on algebraic
expressions in the same manner as we do
in arithmetic.
Algebraic Expressions II
Before we go on to simplification of
algebraic expressions, let us see what 'like
terms' are:
Terms that have the same literal factors
are called
'like terms' otherwise they are called
'unlike terms'
Algebraic Expressions II
 Example:
 5ab, -5ab and 9ab are like terms as they have
the same literal factors ab.
 4x and 5y are unlike terms as their literal factors
are not the same.
 5p and 5q are not like terms though their
numerical coefficients are equal as their literal
factors
p and q are not the same.
Reference
Online Free SAT Study Guide: SAT Guides
http://www.proprofs.com/sat/studyguide/index.shtml