Use binomial expansions to find the expansion in powers of x up to x^4 of (1-x^3)^6 * (1-x)^-6

Question

ganeshie8 · Answer

$\large  (1-x^3)^6 * (1-x)^{-6} $

$\large  (1-x^3)^6 * \frac{1}{(1-x)^{6}} $

$\large   \left( \frac{1-x^3}{1-x} \right)^6  $

ganeshie8 · Answer

$\large   \left( \frac{1^3-x^3}{1-x} \right)^6  $

$\large   \left( \frac{(1-x)(x^2+x+1)}{1-x} \right)^6  $

$\large   \left( x^2+x+1 \right)^6  $

ganeshie8 · Answer

now try expanding

anonymous · Answer

Ok, yes I have expanded that (it's actually the same as another question I've already answered) and it comes out with the right answer. Thank you!

ganeshie8 · Answer

cool :) you did the samy way as above... or any other easy way out ?

anonymous · Answer

Same as your method

ganeshie8 · Answer

okie :)  binomial expansion we cant do for negatives is it

ganeshie8 · Answer

wud the method above, we have to apply binomial theorem two times... and combine like terms which is a pain

ganeshie8 · Answer

was thinking, if there is any easy way...

ganeshie8 · Answer

nvm ! we cant do binomial expansion for negative powers