The binomial theorem and counting principles

Learning objectives

Expand (a + b)ⁿ for positive integer n using Pascal's triangle or the binomial coefficients ⁿCr, and evaluate ⁿCr with and without technology

Find a specific term or coefficient in a binomial expansion, including expansions whose terms involve negative or fractional powers of x

(HL) Use the product rule for counting, permutations and combinations to count arrangements and selections, including problems with restrictions

(HL) Expand (a + b)ⁿ for fractional and negative n as an infinite series, state the values of x for which the expansion is valid, and use it to approximate values