An algebraic expression is a set consisting constants, variables and algebraic operators. It expresses a statement about unknown quantities. An algebraic expression can be solved by simplification, translation, rationalizing, and evaluation. Any of these processes is called an algebraic expression solver.
Simplification of expression is one type of algebraic expression solver. It is always preferable to keep an algebraic expression as short as possible. That is, minimizing the number of terms. There are numerous methods of simplifying an algebraic expression and one must have a good knowledge on algebraic identities, formulas, rules, properties, techniques etc. But more than knowing all these, what is more important is the presence of mind to correctly choose the method and applying the same. let us study a few cases of simplification of expressions.
An expression a2
+ 2ab + b2
can be simplified into a square of a binomial as (a + b)2
The product of sum and difference of two terms (a + b)(a – b) can be simplified as a2
The difference (a + b)2
– (a – b)2
is just 4ab. Simplifications of this type is by using algebraic identities and formulas.
Expressions in the form of a(b + c) are expanded as ab + ac, by using the algebraic property known as ‘distributive property’. This expansion is very useful in certain evaluations.
For example to evaluate 5*(11.13), it is more convenient to rewrite it as 5*(11 + 0.13) and evaluate as 5*11 + 5*0.13 = 55 + 0.65 = 55.65.
It is much more easier than to do a direct multiplication. This is an example of using the algebraic properties and also identifying the correct technique.
Mathematicians framed a number of rules to help us as algebraic expression solver.
For example, as per logarithmic rules, the expression [1 + ½ ln (x) – 3ln (y)] is simplified just as ln [(e√x)/y3)]
We come across number of formulas and thumb rules in the form of algebraic expressions. Formulas may be in the form of equations but an equation contains only expressions on both sides. Here the algebraic expression solver is the translation and proper interpretation of such expressions. You must identify what exactly are the meanings and where are they to be used.
The formula C = (5/9)(F – 32) refers to conversion of temperatures from Fahrenheit scale to Celsius scale.
One must know that F and C denote the temperatures in Fahrenheit and Celsius scales respectively.
Similarly, one must be prompted to understand that the equation c2
is nothing but the Pythagorean identity.
There are certain unwritten rules in algebra which are rigidly followed in practice. Let us examine some of them.
You are not supposed to leave a radical or complex number in the denominator of a rational expression. The algebraic solver in these cases is ‘multiply by the conjugate.
For example, [a]/[(b + √c)] must be rationalized as, [a(b - √c)]/[b2
– c)] by multiplying both top and bottom by (b - √c),
the conjugate of (b + √c).
Similarly an answer should not be left with negative exponents.
f the answer to a problem is ‘x-2
', you are suppose to express that as (1/x2
Evaluation of an expression is assigning the given values of the variables and finding the value of the expression by simplification. In many cases, you have to judge what values are to be assigned to the variable.
Suppose the expression u + 16t gives the final velocity of an object.
You are asked to find the final velocity of an object after 10 seconds if the initial velocity was 40ft/s.
Obviously you need to evaluate the given expression but your subject knowledge must suggest you that the values to be assigned are u = 40 and t = 10.
Thus we find an algebraic equation solver in many forms and identifying the correct algebraic expression solver is your skill.