Mathematics 9709 · AS & A Level · Series
Determine the coefficients of $x^3$ and $x^4$ in the expansion of $(3-ax)^5$, where $a$ is a constant. Express each answer in terms of $a$.
If the coefficient of $x^4$ in the expansion of $(ax+7)(3-ax)^5$ is $240$, determine the positive value of $a$.
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “By using binomial expansion terms like $x^3\cdot\frac{5}{3}\cdot3(-ax)^2(-10\times3^2a^3)$ or $x^4\cdot\frac{5}{4}\cdot3(-ax)^4(5\times3\times4^4)$.” …