Question 110325
Question:

Factor completely

8x cubed - 1

Answer:


{{{ 8x^3 - 1 }}}


This can be written as,


{{{ 2^3 * x^3 - 1^3}}}



==> {{{(2x)^3 - 1^3}}}----------------------------(1)
 which is of the form {{{ a^3 - b^3 }}}


Using the identity,  

{{{ a^3 - b^3 = (a-b)(a^2 + ab + b^2)}}}-------(2)



Comparing (1) and (2), we have, a = 2x and b = 1


So, {{{(2x)^3 - 1^3 = (2x -1)((2x)^2 + 2x * 1 + 1^2) }}} 



==>  {{{(2x)^3 - 1^3 = (2x -1)(4x^2 + 2x + 1 )}}} 




So the factors are, (2x -1) and (4x^2 + 2x + 1)



Hope you found the explanation useful.



Regards.


Praseena.