# Thread: Expand and simplify help?

1. ## Expand and simplify help?

(2a-3b)cubed (i dunno how to make a little 3)

2. Originally Posted by kais
(2a-3b)cubed (i dunno how to make a little 3)

You should know several ways to do this, one is to multiply out:

$\displaystyle ((2a-3b)(2a-3b))(2a-3b)=(4a^2-12ab+9b^2)(2a-3b)=\ ...$

another is to expand using Pascalls triangle/binomial theorem:

$\displaystyle (2a-3b)^3=(2a)^3+3(2a)^2(-3b)+3(2a)(-3b)^2+(-3b)^3=\ ...$

CB

3. Originally Posted by kais
(2a-3b)cubed (i dunno how to make a little 3)

use identity

$\displaystyle (x-y)^3= x^3-y^3-3x^2y+3ab^2$
in this case put x= 2a and y= 3b

4. (a-b)^3=a^3-3ab^2-3ba^2-b^3

5. Hmm,

I'm coming up with 4a squared - 12 ab + 9b still not sure if I'm getting it right though?

6. Originally Posted by kais
Hmm,

I'm coming up with 4a squared - 12 ab + 9b still not sure if I'm getting it right though?
The final result will contain terms of order 3, so there will be terms containing the cube of $\displaystyle a$ and of $\displaystyle b$, as well as terms containing $\displaystyle a^2b$ and $\displaystyle ab^2$

CB

7. Originally Posted by kais
I'm coming up with 4a squared - 12 ab + 9b still not sure if I'm getting it right though?
Post a squared this way : a^2 ; a cubed : a^3

4a^2 - 12ab + 9b^2 is what you get from (2a - b) times (2a - b);
now you need to multiply (4a^2 - 12ab + 9b^2) times (2a - b);
then you're finished.