
Algebraic
Expressions 



Terms, variables, constants 
coefficients

Monomial, binomial, trinomial, . . . , polynomial

Simplifying algebraic
expressions 
Like terms, collecting
or combining like terms 
Evaluating algebraic expressions 






Terms, variables, constants 
coefficients

An
algebraic expression is one or more algebraic terms
containing variables and constants connected by mathematical
operations. 
Terms
are the elements separated by the plus or minus signs. 
In
algebraic expressions, variables are letters, such as a,
b, c,
or x,
y,
z,
that can have different values. 
Constants
are the terms or elements represented only by numbers. 
Coefficients
are the number part of the terms that multiply a variable or
powers of a variable. 

Example: 

a^{2}
 6a
+ 5 
is
the algebraic
expression of three terms, where a
is
the variable, 1 and

6 are
coefficients of the first term and of the middle
term a,
and
5 is the constant.






Monomial, binomial, trinomial, . . . polynomial

An
algebraic expression consisting of a single term is called a
monomial, expression consisting of two terms is binomial, three
terms trinomial and an expression with more than three terms is
called polynomial. 
A
monomial is an expression consisting of a single term, such as 
2a^{3}b. 

Examples: 

 3x^{2}
and
2ab
are monomials, a^{3}
 b^{3}
is
the binomial, 


x^{2
}
4x^{
}+ 4 is
the trinomial, and
a^{3}
 3a^{2
}+
3a
 1
is the polynomial.



Simplifying algebraic
expressions 
By
simplifying an algebraic expression, we mean reducing it in the
simplest possible form which mainly involves: multiplication
and division, removing (expanding) brackets and collecting (adding
and subtracting) like
terms. 
Like
terms are those terms which contain the same powers of same
variables and which can only differ in coefficients. 

Examples: 

a)
 4a^{3
}+
3a^{2
}+
5a^{3
} 7a^{2
} = ( 4
+
5)
· a^{3
}+
(3  7)
· a^{2 } = a^{3 } 4a^{2}, 


b)
(x^{2}^{
} x^{
}+
1)
·
(x
+
1) =
x^{3 } x^{2}
+
x
+
x^{2} ^{
} x^{
}+
1 = x^{3}
+
1. 


Evaluating algebraic expressions 
To
evaluate an algebraic expression means to replace (substitute)
the variables in the expression with numeric values that are
assigned to them and perform the operations in the expression. 

Example: 

Evaluate
the expression x^{2
} 6xy
+
9y^{2}
for x
= 2 and y
= ^{ }1. 
Solution: 

2^{2 } 6
·
2
·
( 1)
+
9
·
(1)^{2}
= 4 +
12 +
9 = 25. 










Beginning
Algebra Contents B 



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