Factoring Expressions

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An algebraically expression is a collection of symbols, it may consist one or more terms, which are separated from each other by signs + and - . Thus   7a + 5b – 3c – x + 2y is an expression consisting of five terms. Expressions are either simple or compound. A simple expression consists of one term, as 5a. A compound expression consists of two or more terms. Thus an expression of two terms, as 3a – 5b is called a binomial expression; one of three terms, as 2a – 3b + c, a trinomial expression; one of more than three terms a multinomial. The solution of algebraic expression when each of the terms composes an expression is divisible by a common factor is given below.
 
Example1. Let us to solve  the terms of the expression 3a2 – 6ab.
Solution :  The terms of the expression 3a2 – 6ab have a common factor 3a,
                   3 a2 – 6ab   = 3 a (a – 2 b)

 Example 2. The terms 5 a2 b x3 – 15ab x2 – 20 b3 x2 has a common factor
                      5 b x2 .
                      5 a2 b x3– 15ab x2 – 20 b3 x2
                      = 5 b x2 (a2 x – 3a – 4 b2 )

Example 3. Resolve into factors  x3 - x2y + xy2
                    x3 - x2y + xy2  =  x (x2 - xy + y2 )
 
Example 4. Resolve into factors 2 x2y3 – 6 x2y2 + 2 xy3
                    2 x2y3 – 6 x2y2 + 2 xy3  = 2 xy (xy2 – 3 xy + y2)
                    =2 xy2 (xy – 3 x + y)
 

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