Your expansion of 1+4x3\sqrt[3]{1+4x}31+4x in ascending powers of x x\,x up to and including x3 x^3\,x3 is 1+43x−169x2+32081x3\displaystyle 1+\frac{4}{3}x-\frac{16}{9}x^2+\frac{320}{81}x^31+34x−916x2+81320x3.
Use your expansion to find an approximation for 1.23\sqrt[3]{1.2}31.2 to 5 decimal places.
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.