That Famous Triangle Could Help
There are two terms in the expansion of ( a + b ) 2 0 1 4 with the highest degree variable of 2012. Find the sum of the coefficients of these two variables.
The answer is 4054182.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
2 solutions
We can view this as ( a + 1 ) 2 0 1 4
The binomial expansion tells us that we will have
a 2 0 1 4 ( 0 2 0 1 4 ) + a 2 0 1 3 ( 1 2 0 1 4 ) + a 2 0 1 2 ( 2 2 0 1 4 )
It's clear that the coefficients of a 2 0 1 2 and 1 2 0 1 2 (aka coefficient a^2) are equal, thus we are looking at 2 ( 2 2 0 1 4 ) = 4 0 5 4 1 8 2
We know that the two variables are a 2 0 1 2 b 2 and a 2 b 2 0 1 2 . Now both of these have the same coefficient ie. C 2 or C 2 0 1 2 . Therefore the answer is 2 × 2 2 0 1 4 × 2 0 1 3 = 2 0 1 4 × 2 0 1 3 = 4054182