(a+b)^3/2 expansion 339456-(a+b)^3/2 expansion
4 Binomial Expansions 41 Pascal's riTangle The expansion of (ax)2 is (ax)2 = a2 2axx2 Hence, (ax)3 = (ax)(ax)2 = (ax)(a2 2axx2) = a3 (12)a 2x(21)ax x 3= a3 3a2x3ax2 x urther,F (ax)4 = (ax)(ax)4 = (ax)(a3 3a2x3ax2 x3) = a4 (13)a3x(33)a2x2 (31)ax3 x4 = a4 4a3x6a2x2 4ax3 x4 In general we see that the coe cients of (a x)n come from the nth row of Pascal'sCity of London Academy 2 4 (a) Find the binomial expansion of in ascending powers of x up to and including the term in x3, simplifying each term (4) (b) Show that, when x = the exact value of √(1 – 8x) is (2) (c) Substitute into the binomial expansion in part (a) and hence obtain an= (a b)(a b)(a b) = (a b)(a² ab ab b²) = (a b)(a² 2ab b²) = a³ 2a²b ab² a²b 2ab² b³ = a³ 3a²b 3ab² b³ Binomial Theorem (a+b)^3/2 expansion
