I need to calculate the sum of coefficients of even powers of $x$ in $$(1+x-2x^2)^6$$

I don't know much about the multinomial theorem, but i know the basics pretty well. I have some ideas of solving such a question for a binomial expansion but that did not work well for multinomial expansions.


Let $$(1+x-2x^2)^6=a_0+a_1x+a_2x^2+\dots+a_{12}x^{12}$$ Substituting $x=1$, $$0=a_0+a_1+a_2+\dots+a_{12}$$ Substituting $x=-1$, $$32=a_0-a_1+a_2-\dots+a_{12}$$ Add the two to get your result.

  • 1
    $\begingroup$ Thanks a lot !..This site is really helpful $\endgroup$ May 1 '15 at 8:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.