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)