Factoring?!?!? 2x^3 + 250 = 2(x^3 + 125) = ...?

[cheyla13]

I am way stuck on this problem :?

2x[sup:2ie8y3px]3[/sup:2ie8y3px]+250

The only thing I know to do is take out the two... or do i even do that???.... unless the back of my textbook is wrong, I dont even know where to start... please help :?

 

[galactus]

Re: Factoring?!?!?

Yes, factor out the 2 and then use the sum of two cubes factorization, \(\displaystyle (x+y)(x^{2}-xy+y^{2})\).

\(\displaystyle 2(x^{3}+125)\)

\(\displaystyle 2(x^{3}+(5)^{3})\)

....\(\displaystyle \uparrow\ \;\ \nearrow\)
....\(\displaystyle \text{x} \;\ \text{y}\)

Now, finish?.