There is no need to learn the binomial expansion of (1+x)^n as far as the GMAT is concerned. You will not be tested on this concept. If they do test this concept, which so far they have not, they will give you the expression for the binomial expansion. If however, you do see a term such as (1+x)^18, then they are expecting you to manipulate the expressions without resorting to binomial expansion.
For example, on the GMAT they could ask the following question:
Given (1+x)^18=27, what is the value of (1+x)^12 ?
Take cube root of the equation (1+x)^18=27, which yields (1+x)^6=3, and then square this to yield (1=x)^12=9.
Such a question is fair game on the GMAT, in fact a similar idea has been tested on the exam.
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