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# 1. In the expansion of \$(ab + bc + ca)^{12}\$, find the coefficient of \$a^9 b^{11} c^4\$.

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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\$.

Mar 8, 2021