In essence, it is a basic understanding for a mathematician to master procedures on how to simplify an algebraic expression before even evaluating it. Apparently, while it may seem different what simplified means to an individual, a simplified algebraic expression has no two ways but a rather coherent conclusion. For an algebraic expression to be simplified then it has to meet a certain mathematical criterion. In this light, a simplified algebraic expression does not have any parenthesis within it, does not have any like times with it, and the constants have to be combined together. For instance, the following expressions are in its simplified form.
(X+3)+3X+1 = 4X+4
5X 2 -3X(X+1) = 2X 2 -3X
Simplifying By Example
5(2+x) +3(5x+4)-(x 2 ) 2
When one wants to simply a particular expression it is always important to try and clear any parenthesis available. Apparently, it is always advisable to utilize the distribution property in clearing the parenthesis which involves multiplying the factors times those terms inside the parenthesis. In this example, the distributive property is used in getting rid of the first set of parenthesis.
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=10 + 5x + 15x +12 – (x 2 ) 2
The second step is to try and remove the parenthesis enclosing the exponents through the use of basic exponent rules. In this case when a particular exponent is raised to a power, then the exponents are multiplied together such that (x 2 ) 2 simplifies to x 4
= 10 + 20x + 12 - x 4
Finally, it is important to look for any existing constants within the expression that can be combined. In this case, 10 and 12 can easily be combined to arrive at 22.
= 22 + 20x - x 4
The expression is now simplified. However, it is usually advisable to set an algebraic expression in a certain way by starting with the factors containing the biggest proponents to constants. By the use of the commutative property of addition, the terms are rearranged while putting the expression in the correct order.
= - x 4 + 20x + 22
