syllabus contentSL 1.9: The binomial theorem: expansion of \({\left( {a + b} \right)^n},\;n \in \mathbb{N}\); use of Pascal"s triangle and \({}_n{C_r}\)HL 1.10: Extension of the binomial theorem to fractional and negative indices, i.e. \({\left( {a + b} \right)^n},\;n \in \mathbb{Q}\)The first significant difference between SL and HL in terms of teaching the binomial theorem arises from the need to calculate binomial coefficients, or combinatorial numbers - that is, combinations of \(n\) items chosen...