Binomial Theorem.

10 lessons89 min4 simulations

This chapter expands a power of a binomial, (a + b)ⁿ, for a positive integer n without multiplying the brackets out. It starts from the patterns in small powers, builds Pascal's triangle and rewrites its entries as nCr, states the binomial theorem and proves it by induction, and then uses the special cases (x − y)ⁿ, (1 + x)ⁿ and (1 − x)ⁿ, the general term, and the theorem's uses in computing powers, estimating and finding remainders.

Also called: binomial expansion · general term