Using complete sentences, explain how you would factor completely $x^9-27$

Question

anonymous · Answer

@Chlorophyll @jim_thompson5910 @phi @Hero

anonymous · Answer

@karatechopper @mattfeury @satellite73 @shadowfiend

anonymous · Answer

@tkhunny

anonymous · Answer

Formula a³ - b³

anonymous · Answer

keeping in mind that this has to be algebra 2 level...just sayin

tkhunny · Answer

For nearly everything that can be expressed like this, $$x^{n} - m^{n}$$, (Certainly assuming x is Real and m and n are integers)  it is true that (x-m) divides it.

That was quite a sentence.

anonymous · Answer

$$x^9-27$$$$x^3\times x^3\times x^3-3^3$$$$\large{x^3}^3 -3^3$$$$\large\text{now what??}$$

anonymous · Answer

This proves that you have no clue about Formula a³ - b³ :P

anonymous · Answer

yes exactly :P ...im soooo confused :(

anonymous · Answer

a³ - b³ = ( a -b) ( a² + ab + b²)
Do yourself a humongous favor, memorize it, will you!

anonymous · Answer

okay but i need to explain in sentences how to do this so....

anonymous · Answer

??

anonymous · Answer

1. Convert the terms into power of 3:
   x^9  = (x³)³ ,  27 = 3³
2. Plug into the formula ( I assume you know it by now ;) )

anonymous · Answer

wait wouldnt it just be $(x^3-3)^3$ ?
$$\left((x^3-3)(x^3-3)(x^3-3)\right)$$

anonymous · Answer

(x³)³ - 3³   =  ( x³ - 3 ) [  (x³)²  + 3x³ + 3² ]
                  =   ....

anonymous · Answer

I LOVE YOU O_O

anonymous · Answer

urm....imma girl too.....so that was just sisterly love..LOL

anonymous · Answer

i got the help i needed, jeez :P ....what an oppressive being :P

anonymous · Answer

=)