Show that (16+10x)12=4(1+58x)12\displaystyle (16+10x)^{\frac{1}{2}} = 4(1 + \frac{5}{8}x)^{\frac{1}{2}}(16+10x)21=4(1+85x)21
Expand (16+10x)12\displaystyle (16+10x)^{\frac{1}{2}}(16+10x)21 in ascending powers of x x\,x up to and including x3x^3x3
Write down the range of values of x x\,x for which the expansion is valid.
Use your expansion, with x=0.1x=0.1x=0.1, to find an approximation of the value of 17 \sqrt{17}\,17 Give your answer to 3 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.