Port Said International Schools – National Section
Better education for future generations
Date : --------------------
Algebraic terms and algebraic expressions
Definitions :
[1]Variable: A variable is a letter or a symbol that represents a number
Ex.: x , y , a , b , ….
[2]Algebraic term: It is forms from the product of two or more factors.
Ex.: 3a , 5y , x2 , 2b , ……
The algebraic term 3x is consists of 2 factors 3(numerical) and x (algebraic)
The algebraic term 4y2 is consists of 3 factors 4(numerical) , y (algebraic) and y (algebraic)
The degree of the algebraic term: It is the sum of the indices (powers) of the algebraic factor
of this term
Ex.:The term 2a is 1st degree because the index of a is 1
The term -7x2 is 2nd degree because the index of x is 2
The term 6a2 b is 2nd degree because the sum of the indices of the two symbols a and b is 3
Important note:
Any number is an algebraic term of zero degree
Ex: The number 4 is an algebraic term of zero degree because it can be written in the form :
4 × xzero where
xzero = 1
[3] Algebraic expression: It consists of an algebraic term ( monomial ) or more.
Ex.: 3y is an algebraic expression consists of one term
3y + 5x is an algebraic expression consists of two terms
3y + 5x + 6 is an algebraic expression consists of three terms
3y + 5x -3xy + 6y is an algebraic expression consists of four terms
Math Department
(monomial)
(binomial)
(trinomial)
(quadrnomial)
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The degree of the algebraic expression: It is the highest degree of the terms forming it.
Ex.: The algebraic expression : 5x – 3 is of the 1st degree because 5x is the term of the highest
degree .
The algebraic expression : 7x2 + 3x – 5y is of the 2nd degree because 7x2 is the term of
the highest degree .
The algebraic expression : 4ab + 2a2b2 + b is of the 4th degree because 2a2b2 is the term of
the highest degree .
Book P: 32
Math Department
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Like algebraic terms
Algebraic terms are similar if the symbols forming its factors are similar and the indices
of these symbols are similar
Examples of like terms:
 2a , 4a , -6a
 3x2 , 4x2 , -2x2
 2x2y , 4yx2 , - 5x2y
Examples of unlike terms:
 2x , 3x2 , 4x3
(their indices are different)
2
2
 4x , 5xy , -y
(their symbols are different )
Adding and subtracting like terms
When adding or subtracting like terms , we add or subtract the coefficients of these
terms while the algebraic factors stay as they are
Ex.: Add:
 5a + 3a + a = (5+3+1) a = 9a
 7ab2 +(-2b2a) + 4ab2 + b2a
= [ 7 + (-2) + 4 + 1 ] ab2 = 10ab2
Subtract 5xy from 7xy
 7xy – 5xy = (7 – 5 ) xy
=2xy
3
Subtract-3x y from -2yx3
 -2yx3 – ( -3x3y ) = (-2 + 3 ) yx3
= yx3
Simplifying the algebraic expression:
The simplest form of the algebraic expression means all its terms are unlike , so we will put it
in the simplest form by adding like terms using commutative and associative properties.
Ex.: Simplify:
 6x + 7y + 4x – 3y
= 6x + 4x + 7y – 3y
= (6x + 4x ) + ( 7y – 3y )
= 10x + 4y
Math Department
( commutative )
( Associative )
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Book P: 34
Math Department
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