Expand \( \log _{\frac{1}{2}}\left(\frac{3 x^{2}}{2}\right) \) using the properties and rules for logarithms. (1 point) \( \log _{\frac{1}{2}}(3)+2 \log (x)-\log _{\frac{1}{2}}(2) \) \( \log _{\frac{1}{2}}(3)+2 \log _{\frac{1}{2}}(x)+1 \) \( 2 \log _{\frac{1}{2}}(3 x)+1 \) \( \log _{\frac{1}{2}}(3 x)-\log _{\frac{1}{2}}(2) \)

(116) \( 3(\sqrt{3}+\sqrt{6})^{2}-(\sqrt{14}+\sqrt{7})^{2}-6 \)

\( 117)(5 \sqrt{2}+3)(5 \sqrt{2}-3)-(14 \sqrt{3}-1)-7(\sqrt{1,5}-\sqrt{2})^{2} \).

Find a degree 3 polynomial with real coefficients having zeros 3 and \( 3 i \) and a lead coefficient of 1 . Write \( P \) in expanded form. \( P(x)=\square \)

Compute each sum below. If applicable, write your answer as a fraction. \( 2+2(-2)+2(-2)^{2}+\ldots+2(-2)^{7}=\square \) \( \sum_{k=1}^{9}\left(\frac{1}{3}\right)^{k}=\square \)

Middle term of expansion \[ \left(3 x-\frac{x^{3}}{6}\right)^{9} \]