3.2 Monomials, Polynomials and Factoring
Monomial : An algebraic expression which contains only one term is called the monomial expression. For example
Binomial : An algebraic expression consisting of two terms is called a Binomial expression. For example, ( 4 a + 5 b ),
Similarly, we can define trinomial etc.
Like terms
: Terms which involve the same letter
and the same index ( i.e. power ) are ‘like terms’ . For example 2a and
3 a , ,
, 3 xy and  xy etc.
Addition and Subtraction of Monomials :
To add or subtract monomials, use the same rules as with directed (signed) numbers, provided the terms are alike.
Example Add 20 a^{2} b c + 4 a^{2} b c
Solution : 20 a^{2} b c + 4 a^{2} b c = ( 20 + 4 ) a^{2} b c
= 24 a^{2} b c
Note that the addition of like terms is done by adding their coefficients (taken with their signs ) and multiplying this sum by the common letter or letters.
Perform the operations indicated :
Example 7 x  2 x
Solution : 7 x  2 x = ( 7  2 ) x
= 5 x
Example 10 x^{2} + 3 x^{2}  5 x^{2}
Solution : 10 x^{2} + 3 x^{2}  5 x^{2} = ( 10 + 3  5 ) x^{2}
= 8 x^{2}
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