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.
Show that the first three terms of the binomial expansion of f(x)f(x)f(x) are 1+12ax−18a2x2\displaystyle 1 + \frac{1}{2}ax - \frac{1}{8}a^2x^21+21ax−81a2x2.
Hence find the value of aaa.
Using this value of aaa, state the set of values for which the binomial expansion is valid.
Using this value of aaa, 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.