\(\sqrt{18}-2\sqrt{32}+3\sqrt{50}-4\sqrt{8}\)

\(=3\sqrt{2}-8\sqrt{2}+15\sqrt{2}-8\sqrt{2}\)

\(=-5\sqrt{2}+15\sqrt{2}-8\sqrt{2}\)

\(=10\sqrt{2}-8\sqrt{2}\)

\(=2\sqrt{2}\)

\(\sqrt{2\cdot2^2+4^2+5^2}\)

\(=\sqrt{2\cdot4+16+25}\)

\(=\sqrt{8+16+25}\)

`=`\(\sqrt{49}\)

`=7`

a) \(x^3-25x=0\)

\(\Leftrightarrow x\left(x+5\right)\left(x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-5\\x=5\end{matrix}\right.\)

`=>`\(x\in\left\{0;-5;5\right\}\)

b) \(4x\left(x+1\right)=8\left(x+1\right)\)

\(\Leftrightarrow4x^2+4x=8x+8\)

`<=>`\(4x^2+4x-8x=8\)

`<=>`\(4x^2-4x=8\)

`<=>`\(4x^2-4x-8=0\)

`<=>`\(4\left(x-2\right)\left(x+1\right)=0\)

`<=>`\(\left(x-2\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\) 

`=>`\(x\in\left\{2;-1\right\}\)

c) \(4-x=4\left(x-4\right)^2\)

`<=>`\(4-x=4x^2-32x+64\)

\(\Leftrightarrow4-x-4x^2+32x-64=0\)

\(\Leftrightarrow4+31x-4x^2-64=0\)

\(\Leftrightarrow-60+31x-4x^2=0\)

\(\Leftrightarrow4x^2-16x-15x+60=0\)

\(\Leftrightarrow4x\left(x-4\right)-15\left(x-4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\4x-15=0\end{matrix}\right.\)

`=>`\(x\in\left\{\dfrac{15}{4};4\right\}\)

\(\dfrac{\left(2x^3-5x^2+6x-15\right)}{\left(2x-5\right)}\)

\(=\dfrac{\left(2x-5\right)\cdot\left(x^2+3\right)}{\left(2x-5\right)}\)

\(=x^2+3\)

`a)` \(\left(\dfrac{4}{15}+\dfrac{3}{5}\right):\dfrac{5}{6}+\left(\dfrac{11}{15}-\dfrac{8}{5}\right):\dfrac{5}{6}\)

\(=\left(\dfrac{4}{15}+\dfrac{9}{15}\right)\cdot\dfrac{6}{5}+\left(\dfrac{11}{15}-\dfrac{24}{15}\right)\cdot\dfrac{6}{5}\)

\(=\dfrac{13}{15}\cdot\dfrac{6}{5}-\dfrac{13}{15}\cdot\dfrac{6}{5}\)

\(=\dfrac{6}{5}\cdot\left(\dfrac{13}{15}-\dfrac{13}{15}\right)=0\)

`b)` \(\left(\dfrac{7}{15}-\dfrac{7}{5}+\dfrac{8}{15}+\dfrac{2}{5}\right)\cdot\dfrac{2021}{2022}\)

\(=\left(\dfrac{7}{15}-\dfrac{21}{15}+\dfrac{8}{15}+\dfrac{6}{15}\right)\cdot\dfrac{2021}{2022}\)

`=0*2021/2022=0`

`c)` \(\left(1+\dfrac{2}{3}-\dfrac{1}{4}\right)\cdot\left(\dfrac{4}{5}-\dfrac{3}{4}\right)^2\)

\(=\left(\dfrac{12}{12}+\dfrac{8}{12}-\dfrac{3}{12}\right)\cdot\left(\dfrac{16}{20}-\dfrac{15}{20}\right)^2\)

\(=\dfrac{17}{12}\cdot\dfrac{1}{400}\)

`=17/4800`

\(f)\) \(3\cdot5^2-27:3^2+5^2\cdot4-18:3^2\)

\(=3\cdot25-27:9+25\cdot4-18:9\)

\(=75-3+100-2\)

\(=175-5\)

`=170`

\(16x^2-1=0\)

\(16x^2=1\)

\(x^2=\dfrac{1}{16}\)

`=>`\(\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=-\dfrac{1}{4}\end{matrix}\right.\)

\(\dfrac{\sqrt{22}}{\sqrt{11}}+\sqrt{8}-\dfrac{7\sqrt{2}}{3-\sqrt{2}}\)

\(=\sqrt{2}+\sqrt{8}-\dfrac{7\sqrt{2}}{3-\sqrt{2}}\)

\(=3\sqrt{2}-\dfrac{7\sqrt{2}}{3-\sqrt{2}}\)

\(=-2\)

\(9x-2\cdot3^2=3^4\)

\(9x-2\cdot9=81\)

\(9x-18=81\)

\(9x=81+18\)

\(9x=99\)

`=>x=99/9=11`

\(123+60:\left[16-2\left(5^2-20\right)\right]\)

\(=123+60:\left[16-2\left(25-20\right)\right]\)

\(=123+60:\left(16-10\right)\)

\(=123+60:6\)

`=123+10`

`=133`