What is the binomial theorem and why is it true?
The binomial theorem is an algebraic formula for the expansion of powers of an expression with two terms (a binomial). For example, we can use it to calculate the polynomial expansion of, say, (1+x)^n for any value of n. The theorem states that (a+b)^n = (involving binomial coefficients).
This formula can be derived by thinking about what the binomial coefficients actually represent. The binomial coefficient nCr represents the number of ways of picking r terms from a total of n terms. .
Sample questions involving this formula might include:
-Write a full polynomial expansion for (2+3x)3
-Find the coefficient of x4 in (x-1)7
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