Find the first 4 terms, in ascending powers of xxx, of the binomial expansion of
(3+kx9)6\left(3 + \frac{kx}{9}\right)^6(3+9kx)6
where kkk is a non-zero constant. Give each term in its simplest form.
Given that
f(x)=(4+2x)(3+kx9)6f(x) = (4 + 2x)\left(3 + \frac{kx}{9}\right)^6f(x)=(4+2x)(3+9kx)6
and that in the expansion of f(x)f(x)f(x), the coefficient of xxx is equal to the constant term, find the value of kkk.
Practise Edexcel A Level Maths 4.2 Expanding (a + bx)^n with exam-style questions for A Level Maths. 99 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.