# Thread: Simplifying: sum of two cubes

1. ## Simplifying: sum of two cubes

I haven't done this in over 20 years. I'm going back to get a degree in a field i've always dreamed and this is throwing me off.

The book reads "These exercises involve factoring by grouping and factoring sums and differences of cubes. Write each rational expression in lowest terms. I used ^ for the exponent.

the question is

1+ p^3
_______
1 + p

2. Originally Posted by Tenskypoo
I haven't done this in over 20 years. I'm going back to get a degree in a field i've always dreamed and this is throwing me off.

The book reads "These exercises involve factoring by grouping and factoring sums and differences of cubes. Write each rational expression in lowest terms. I used ^ for the exponent.

the question is

1+ p^3
_______
1 + p
note that we can think of $\displaystyle 1 + p^3$ as $\displaystyle 1^3 + p^3$. that is, as the SUM of two cubes.

here is the formula, see what you can do with it: $\displaystyle a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

3. i got 1-p + p^2

4. Originally Posted by Tenskypoo
i got 1-p + p^2
yes

$\displaystyle \frac {1 + p^3}{1 + p} = \frac {(1 + p)(1 - p + p^2)}{1 + p} = 1 - p + p^2$ ....since the (1 + p)'s cancel

5. Originally Posted by Jhevon
here is the formula, see what you can do with it: $\displaystyle a^3 + b^3 = (a + b)(a^2 - ab + b^2)$
To the original poster: Make sure you memorize the above formula before the next test!