Question

I need help with binomial expansion pls, the question is attached

Answer 1

`\\\left(a + b\right)^(n) = \\ \sum_(k=0)^(n) {\binom{n}{k}} a^(n - k) b^(k) \\ \left(2 - 9 x\right)^(4) = \\ 16 - 288 x + 1944 x^(2) \\ - 5832 x^(3) + 6561 x^(4) \\ = 16 - 288 x + 1944 x^(2)\\ A - 232 x + B x^(2) \\ \therefore A=16 \\ (1+kx)(16 - 288 x + 1944 x^(2))\\ 16kx -288x =-232x \\ 16k=56 \\ \therefore k=(7)/(2)\\ B =1944-288( (7)/(2) )\\\therefore B=936`

All you have to do is compare coofficients...