Show that the expansion of (9−2x)12\displaystyle (9 - 2x)^{\frac{1}{2}}(9−2x)21 in ascending powers of xxx, up to and including x3x^3x3, is 3−13x−154x2−1486x3\displaystyle 3 - \frac{1}{3}x - \frac{1}{54}x^2 - \frac{1}{486}x^33−31x−541x2−4861x3.
Write down the range of values of x x\,x for which the expansion is valid.
Use your expansion, with a suitable value of xxx, to find the value of 8.9 \sqrt{8.9}\,8.9 correct to 5 significant figures
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.