ALGEBRA TERMS :
EXPLANATION WITH EXAMPLES
Please study
Algebra Symbols before Algebra Terms
if you have not already done so.
Algebra Terms before Algebraic Expression :
Before going to study Algebraic Expression,
we need to know about term.
Term in Basic Algebra :
Numerical numbers alone or literal numbers alone or
their combinations by operation of multiplication (or division) are called terms.
Here even if you don't mention division, it is ok
because division is nothing but multiplying with reciprocal.
Examples: 3, -7, 2⁄5, a , x , abc , 6n, -8p, xy , m⁄6 are all terms.
In 2⁄5, 2 is divided by 5. (or we can say 2 is multiplied by 1⁄5)
similarly, In m⁄6, m is divided by 6. (or we can say m is multiplied by 1⁄6)
A combination of terms obtained by the operations of '+' or '-' or both
is called an algebraic expression.
We may also say that
The several parts of an algeraic expression seperated by '+' or '-' sign
are called the TERMS of the expression.
Examples:
(i) 5a + 3b,
(ii) 4x - 7yz,
(iii) 2p + 3q - 3r⁄5,
(iv) lx⁄2 + my⁄3 - nz
are all Algebraic Expressions.
Example (i) is obtained by adding the terms 5a and 3b .
Example (iv) is obtained by combining the terms
lx⁄2, my⁄3 and nz ,
using '+' and '-' symbols.
while writing the terms we write them with thier sign of '+' or '-'.
Since + is the default sign, it need not be written for the term.
But '-' is to be written specifically.
For example,
The terms of example (ii) are 4x and -7yz.
The terms of example (iii) are 2p, 3q and -3r⁄5.
Note that multiplication and division do not seperate terms.
Where as addition and subtraction seperate terms.
Thus, xy or x⁄y is one term,
while x + y or x - y are two terms.
Factors of a term in Algebra Terms:
When numbers and literals are multiplied to form a product, then
each quantity multiplied is called a factor of the product.
A constant factor is called a numerical factor while
a variable factor is called a literal factor.
Example:
consider the algebraic expression 7xy - 6a2b.
There are two terms: 7xy and -6a2b.
In the first term 7xy :
The numerical factor is 7.
The literal factors are x, y, xy.
In the second term -6a2b:
The numerical factor is -6.
The literal factors are a, a2, b , ab and a2b.
Constant Term of Algebra Terms :
A term of the expression having no literal factor is called the constant term.
Examples:
In the expression 2x - y + 8, the constant term is 8.
In the expression 2x2 - 2y2 + xy - 9, the constant term is -9.
Coefficient in Algebra Terms :
In a product containing two or more factors, each factor is called
the coefficient of the product of other factors.
In particular, the constant part is called the numerical coefficient of the term and the remaining part is called the literal coefficient of the term.
Example:
In the term 7xy,
Numerical coefficient of the term = 7.
Literal coefficient of the term = xy.
Coefficient of xy = 7.
Coefficient of x = 7y.
Coefficient of y = 7x.
When the numerical coefficient of a term is +1 or -1,
it will not be written.
Thus 1x is written as x
and -1x is written as -x.
Like and Unlike terms of Algebra Terms :
Terms which contain the same literal factor are called like terms.
Otherwise they are called unlike terms
Following simple steps will help you to decide
whether the given terms are LIKE or UNLIKE terms.
- Ignore the numerical coefficients.
Concentrate on the algebraic part of the terms.
- Check the variables in the terms. They must be the same.
- Next. check the powers of each variable in the terms.
They must be the same.
- Ignore the order in which the variables
are multiplied in the terms.
Examples:
(i) 8xy, -9xy, xy are like terms. (variables and their
powers are the same.)
(ii) -3ab2, 9b2a, ab2 are like terms.
(variables and their powers are the same.)
(iii) 4x, -9xy are unlike terms.
(variables are different.)
(iv) -3ab2, 9a2b, are unlike terms.
(powers of variables are different.)
There are a list of Algebra Terms pertaining
to Algebraic Expressions. These are
provided with accompanying definitions
along with Examples at
Algebra Glossary
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