The function f(x)f(x)f(x) is given by f(x)=1+axf(x) = \sqrt{1 + ax}f(x)=1+ax where a a\,a is a non-zero constant. In the binomial expansion of f(x)f(x)f(x), the coefficients of x x\,x and x2 x^2\,x2 are equal.
Find the value of a a\,a and, using this value of aaa, state the set of values for which the binomial expansion is valid and write down the quadratic function that approximates f(x)f(x)f(x) when x x\,x is small.
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.