1. In the expansion of $(ab + bc + ca)^{12}$, find the coefficient of $a^9 b^{11} c^4$.
2.Find the coefficient of $u^2 v^9$ in the expansion of $(2u^2 - 3v^3)^4$.
3. Expand $(2x - 1)^5$.
4. For some real number $a$ and some positive integer $n$, the first few terms in the expansion of $(1 + ax)^n$ are \[1 - 20x + 150x^2 + cx^3 + \dotsb.\]Find $c$.
5. Let $a$ and $b$ be real numbers such that $a^3 + 3ab^2 = 679$ and $3a^2 b + b^3 = -652$. Find $a + b$.
