求下列各展开式中与 $x$ 无关的项。

(a) $\big(3x+\frac2{x^2}\big)^6$

(b) $\big(3x+\frac2{x^2}\big)^6(1-x^3)$

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

每从括号里多选一个 $2/x^2$，总指数就减少 $3$。先确定要选几次。

Choosing $2/x^2$ a total of $j$ times gives the term $\binom6j3^{6-j}2^jx^{6-3j}$. The constant term uses $j=2$ and is

乘以 $-x^3$ 后，原展开式的 $x^{-3}$ 项也会变成常数。用 (a) 的指数规律找它。

The original constant contributes $4860$. To obtain an additional constant from the factor $-x^3$, we need $6-3j=-3$, giving $j=3$. The coefficient of $x^{-3}$ is $\binom63 3^3 2^3=4320$, and it contributes $-4320$. The required constant is $4860-4320=540$.