# Thread: Sum of Two cubes

1. ## Sum of Two cubes

2. Originally Posted by Webby
Hi I am having a few problems with a couple of questions of an algebra revision assignment. I have never heard of, nor been taught how to do the sum of two cubes up until this point.

a) 54x^3 +2
b) x^6 -7x^3 -8

I have been having a go with the first one as it seems simpler. Using the theory I have found on wikipedia . a^3 + b^3 = (a+b)(a^2 -2ab + b^2) I have tried to *fudge* an answer but it isnt working out when I expand it to check my work.

a) 2(27x^3 +1)
2(1+3x)(9x^2 -6y+1)

This is where I come to trying to jam it into a formula, however through not knowing what to do or making a blind mistake it doesnt seem to be correct.
I have no idea where to start with the second problem, seeing as I cannot do a much easier question. Any help is much appreciated
hi

(1) $\displaystyle 2(27x^3+1)=2[(3x)^3+1^3]$

$\displaystyle =2[(3x+1)(9x^2-3x+1)]$

(2) Let x^3 be p so that it's easier for you to see.

$\displaystyle p^2-7p-8=(p-8)(p+1)=(x^3-8)(x^3+1)$