# Thread: Simplifying: difference of two cubes

1. ## Simplifying: difference of two cubes

$
\frac {x^2 - 27}{x - 3}
$

2. Originally Posted by Tenskypoo
$
\frac {x^2 - 27}{x - 3}
$
based on your previous questions, it makes me feel this should be $\frac {x^3 - 27}{x - 3}$ ...is that right?

3. yup. I've gotten to where it is

(x+27)(x^2 - (x times 27))+ 27^2
__________________________________
x-3

4. Originally Posted by Tenskypoo
yup. I've gotten to where it is

(x+27)(x^2 - (x times 27))+ 27^2
__________________________________
x-3

nope

ok, so if it is $x^3 - 27$ on top. you would write that as $x^3 - 3^3$ and apply the (difference of two cubes) formula: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

5. ah, because 3 x 3 x 3= 27

So if it was, x^4 - 16 it would be x^4 - 2^4 just as an example to see if i understand.

6. Originally Posted by Tenskypoo
ah, because 3 x 3 x 3= 27

So if it was, x^4 - 16 it would be x^4 - 2^4 just as an example to see if i understand.
ah, yeah, you could write it like that. but the formula i gave does not apply to that expression. but yes, that's the idea

7. Originally Posted by Jhevon
nope

ok, so if it is $x^3 - 27$ on top. you would write that as $x^3 - 3^3$ and apply the (difference of two cubes) formula: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$
so would it be

x^3 - 3^3 = (x - 3)(x^2 + (x times 3) + 3^2)

8. Originally Posted by Tenskypoo
so would it be

x^3 - 3^3 = (x - 3)(x^2 + (x times 3) + 3^2)
yes, that's the numerator

9. i'd put that over x-3, but cancel out the x-3 since it is in both the numer. and denom. therefore leaving me with

$x^2 + 3x + 9$

i may have done the part wrong, or it isn't simplified enough

10. Originally Posted by Tenskypoo
i'd put that over x-3, but cancel out the x-3 since it is in both the numer. and denom. therefore leaving me with

$x^2 + 3x + 9$

i may have done the part wrong, or it isn't simplified enough
that is fine

11. Originally Posted by Tenskypoo
yup. I've gotten to where it is

(x+27)(x^2 - (x times 27))+ 27^2
__________________________________
x-3

Make sure you learn and memorize the formula for factoring a difference of cubes before the next test!