Saturday, April 25, 2015

Use the Binomial Theorem to expand and simplify the expression.

You need first to factorize , such that:




 


You need to use the binomial formula, such that:



You need to replace 4x for x, 1 for y and 3 for n, such that:



By definition, nC0 = nCn = 1, hence

You need first to factorize , such that:




 


You need to use the binomial formula, such that:



You need to replace 4x for x, 1 for y and 3 for n, such that:



By definition, nC0 = nCn = 1, hence


By definition nC1 = nC(n-1) = n, hence



Replacing the binomial expansion  for   yields:




Grouping the like terms yields:



Hence, expanding and simplifying the expression yields

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