The expansion of (a+bx)13\displaystyle (a+bx)^{\frac{1}{3}}(a+bx)31 in ascending powers of x x\,x up to and including x3 x^3\,x3 is 2+x−12x2+512x3\displaystyle 2+x-\frac{1}{2}x^2+\frac{5}{12}x^32+x−21x2+125x3. Find the values of a a\,a and bbb.
Write down the range of values of x x\,x for which the expansion is valid.
408 exam-style questions on Edexcel A Level Maths Binomial Expansion, covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions. Each one has a worked solution and a mark scheme showing where the marks go.