\(1,\\ a,=3x\left(1-3y\right)\\ b,=9xy\left(2xy-x^2+4y\right)\\ c,=\left(x-y\right)\left(15x-5y\right)=5\left(x-y\right)\left(3x-y\right)\\ 2,\\ a,\Rightarrow2x^2\left(x^2-4\right)=0\Rightarrow2x^2\left(x-2\right)\left(x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-2\end{matrix}\right.\\ b,\Rightarrow\dfrac{2}{5}x\left(x+10\right)-\left(x+10\right)=0\\ \Rightarrow\left(x+10\right)\left(\dfrac{2}{5}x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-10\\\dfrac{2}{5}x=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-10\\x=\dfrac{5}{2}\end{matrix}\right.\)
\(3,\)
\(a,\left\{{}\begin{matrix}AK=KD\\BI=IC\end{matrix}\right.\Rightarrow KI\) là đtb hình thang ABCD
\(b,\) Vì KI là đtb hình thang ABCD nên \(KI=\dfrac{AB+CD}{2}=\dfrac{17}{2}=8,5\left(cm\right)\)
\(c,\) \(\left\{{}\begin{matrix}AK=KD\\KE//AB\end{matrix}\right.\Rightarrow BE=ED\Rightarrow KE\) là đtb tam giác ABD
\(\Rightarrow KE=\dfrac{1}{2}AB=2,5\left(cm\right)\)
\(\left\{{}\begin{matrix}BI=IC\\IF//AB\end{matrix}\right.\Rightarrow AF=FC\Rightarrow IF\) là đtb tam giác ABC
\(\Rightarrow IF=\dfrac{1}{2}AB=2,5\left(cm\right)\)
Ta có \(EF=KI-KE-IF=8,5-2,5-2,5=3,5\left(cm\right)\)
