Factoring Expressions

Factoring Expressions 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)