Question

What is the sum of the coefficients of
( [3x - 3x^2 +1]^744 ) x ( [- 3x + 3x^2 +1]^745 ) ??

Answer 1

i bet we can do this, i need paper

Answer 2

Good problem.

Answer 3

Thanks I Know Its Hard

Answer 4

hmm i was thinking along the lines of
\[(1+a)(1-a)=1-a^2\] with
\[a=x^2-3x\] but that did't get me too far yet

Answer 5

oh

Answer 6

oh hold the phone. sum of coefficients is what you get when x = 1

Answer 7

wow your smart :)

Answer 8

so we can write as
\[






































































































































































































































































































\[1-9 (x^2-x)^2\]

Answer 9

:)

Answer 10

that is
\[(3x - 3x^2 +1 ) \times(- 3x + 3x^2 +1)=1-9(x^2-x)^2\] right?

Answer 11

then raise to the power of whatever, say 755 and get
\[(1-9(x^2-x)^2)^{755}\]

Answer 12

how am i doing so far?

Answer 13

wow :O your smart thanks

Answer 14

:)

Answer 15

replace x by 1, get 1

Answer 16

so the answer is 1?

Answer 17

oh wait you have another term but you can cope with that

Answer 18

alright

Answer 19

\[(1-9(x^2-x)^2)^{744}(- 3x + 3x^2 +1)\] is what you have

Answer 20

replace x by 1, first term gives 1, second one gives ... 1 as well
so i guess the answer is 1

Answer 21

probably was an easier way to do it. repost and i bet you will get one

Answer 22

thanks :)