Identify parts of an expression :
Here we are going to see how to identify the parts of an algebraic expression.
In an algebraic expression, we may find the following three parts.
(i) Terms
(ii) Factors
(iii) Coefficients
What is term ?
A single variable or a constant or a combination of these as a product or quotient forms a term.
Examples of terms :
5, a, 3ab, 21/7, ........... etc
Terms can be added or subtracted to form an expression.
What is factor ?
Consider the expression 3ab – 5a. It has two terms 3ab and 5a. The term 3ab is a product of factors 3, a and b. The term 5a is a product of 5 and a. The coefficient of a variable is a factor or factors.
Example :
In the term 3ab;
(i) the coefficient of ab is 3 (ii) the coefficient of a is 3b
(iii) the coefficient of b is 3a.
In the term –5a the coefficient of a is –5
What is constant ?
A number which is not having any variable with it is known as constant.
Example 1 :
Identify the parts of the following expression
2x + 3
Solution :
In the expression 2x + 3 the term 2x is made of 2 factors and 2 and x while 3 is a single factor.
Example 2 :
Identify the parts of the following expression
3ab  5a
Solution :
Example 3 :
Identify the number of terms and coefficient of each term in the expression.
x^{2} y^{2}  5 x^{2} y + (3/5) xy^{2}  11
Solution :
In the given expression, we have four terms.
Term 1 ==> x^{2} y^{2}
Term 2 ==>  5 x^{2} y
Term 3 ==> (3/5) xy^{2}
Term 4 ==> 11
Coefficient of 1st term = 1
Coefficient of 2nd term = 5
Coefficient of 3rd term = 3/5
Since the last term is not having any variable, it is a constant term.
Example 4 :
Identify the number of terms, coefficient and factors of each term in the expression.
3abc  5ca
Solution :
The given expression contains two terms.
Term 1 ==> 3abc
Term 2 ==> 5ca

Terms 
Coefficients 
Factors 
1) 
3abc 
3 
a, b and c 
2) 
5ca 
5 
c and a 
Example 5 :
Identify the number of terms, coefficient and factors of each term in the expression.
1 + x + y^{2}
Solution :
The given expression contains three terms.
Term 1 ==> 1
Term 2 ==> x
Term 2 ==> y^{2}

Terms 
Coefficients 
Factors 
1) 
1 
 
 
2) 
x 
1 
x 
3) 
y^{2} 
1 
y and y 
Example 6 :
Identify the number of terms, coefficient and factors of each term in the expression.
3x^{2} y^{2}  3xyz + z^{3 }
Solution :
The given expression contains three terms.
Term 1 ==> 3x^{2} y^{2}
Term 2 ==>  3xyz
Term 2 ==> z^{3 }

Terms 
Coefficients 
Factors 
1) 
3x^{2} y^{2} 
3 
x^{2} and y^{2} 
2) 
 3xyz 
3 
x, y and z 
3) 
z^{3 } 
1 
z, z and z 
Example 7 :
The coefficient of x^{4} in 5x^{7} + (3/7) x^{4}  3x^{3} + 7x^{2}  1
Solution :
The coefficient of x^{4 }is 3/7.
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