Aiden W.

asked • 05/18/16

how do you simplify a cubed variable?

ex. 3x^3+27x
 
thank you for any help

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Inactive Tutor answered • 05/18/16

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The first thing you should do when factoring any polynomial expression is to factor out any monomial common to all terms, in this case 3x.
 
(3x) (x2+9)
 
In the realm of reals this expression is irreducible.
 
In complex numbers it can be further reduced to:
 
(3x) (x+3i)(x-3i)
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Inactive Tutor

If your expression had not resolved so readily, you would then want to look and see if you are dealing with the sum of two cubes, the difference of two cubes, or pattern indicating a perfect cube of a binomial (coefficients  following the pattern 1,3,3,1 or , 1,-3,3,-1).  Finally there is a pattern where the ratio of the first and third coefficients is the same as the ratio of the second and fourth coefficients, in such a case you can factor by "grouping" and using the distributive law.  
 
If none of these options work, the problem is much harder.
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05/18/16

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