Use binomial expansion to show that 1+6x1−x≈1+72x−218x2\displaystyle \sqrt{\frac{1+6x}{1-x}} \approx 1 + \frac{7}{2}x - \frac{21}{8}x^21−x1+6x≈1+27x−821x2. Hence, substitute x=18\displaystyle x = \frac{1}{8}x=81 into the expansion to obtain an approximation for 8\sqrt{8}8. Give your answer as a fraction in its simplest form.
A student substitutes x=12\displaystyle x = \frac{1}{2}x=21 into the expansion to find an estimate for 8\sqrt{8}8. Give a reason why the student should not use x=12\displaystyle x = \frac{1}{2}x=21.
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.