Monday, November 26

Simplifying Algebraic Expressions

Algebraic expressions are the representations in order to neglect writing in terms of words of relation between various terms. There are two variations in algebraic expressions which can be said as the rational and irrational algebraic expressions. A rational expression is nothing but an algebraic expression which can be written in a quotient of polynomials, for example x2 + 2x + 4. Meanwhile, an irrational expression is the one that in which is not rational, for example square root of (x+4).

Algebra Simplifying Expressions
In general, the algebraic expressions contain numbers and alphabetic symbols. Simplifications of some lengthy algebraic expressions are needed in order to shorten and solve the problem. While making that simplification, an equivalent expression would be finally arrived which is simpler than the previous. It obviously means that the simplified expression is smaller than the normal.

How to simplify Algebraic Expressions?

  • There are no standard procedures for the simplification of algebraic expressions since there can be so many methods can be made which differ from person to person while doing. But, those can be grouped in some form as three types as follows.
  • Expressions which can be simplified without any kind of preparation immediately.
  • Expressions which requires preparation before doing the simplification.
  • Expressions which cannot be simplified to any form.
  • Also there are some rules are methods that can be used while doing the simplification. Before going into the example for simplifying, we shall see some of the rules while doing them.
  • While doing the addition of fractions:  When the denominator is common for all the fractions, then add all the numerators and sum it and divide it by the common denominator.
  • Simplify the expression as much as possible to the extent.
  • Order of Expression: When there are confusingly operations were given, for example 8+4(2+3)2-7, then the order of doing simplification as follows. 1) Simplify the terms inside the parenthesis 2) Evaluate the powers and exponents if it is there, 3) Multiply or divide 4) Add or subtract. 

Examples of simplifying Algebraic Equations

  • The below some examples would give an idea of how to simplify expressions. 2 x+3y+6-3x-2y-2+4yx. This expression can be easily simplified by adding all the like terms and combining finally. Hence it can be rewritten as (2-3+4) x + (3-2) y + (6-2) and finally it gives 3x+y+4.
  • To simplify the expression of previously said example of 8+4(2+3)2-7, after first process we will get, 8+4(5)2-7, then 8+4(25)-7, then 8+100-7 and finally we will get answer as 101.

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