\(1.\\ a,4x\left(x-3y\right)+5x\left(2y-x\right).\\ =4x^2-12xy+10xy-5x^2.\\ =-x^2-2xy.\)

Thay \(x=1,y=-1:\)

\(-1^2-2.1.\left(-1\right).\\ =1\)

\(b,\dfrac{-1}{2}x\left(x^2-3x+y\right)-5x^2\left(x+2y\right).\\ \)

Thay \(x=2,y=3:\)

\(\dfrac{-1}{2}2\left(2^2-3.2+3\right)-5.2^2\left(2+2.3\right).\\ =-161.\)

\(c,6x\left(x+y\right)+\left(4x-7\right)\left(x-2y\right).\\ =6x^2+6xy+4x^2-8xy-7x+14y.\\ =10x^2-2xy-7x+14y.\)

\(2.\\a,4x\left(x-3\right)-2x\left(2x+5\right)=7\left(x-3\right).\\ \Leftrightarrow 4x\left(x-3\right)-2x\left(2x+5\right)-7\left(x-3\right)=0.\\ \Leftrightarrow4x^2-12x-4x^2-10x-7x+21=0.\\ \Leftrightarrow-29x+21=0.\\ \Leftrightarrow x=\dfrac{21}{29}.\)

\(a,\left(2x-3\right)^2=25.\\ \Leftrightarrow\left[{}\begin{matrix}\left(2x-3\right)^2=5^2.\\\left(2x-3\right)^2=\left(-5\right)^2.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=5.\\2x-3=-5.\end{matrix}\right.\)

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

\(b,\dfrac{27}{3^x}=3.\\ \Leftrightarrow3^x=9.\\ \Leftrightarrow3^x=3^2.\\ \Rightarrow x=2.\)

\(c,\left(\dfrac{8}{3}-2x\right)^4=625.\\ \Leftrightarrow\left[{}\begin{matrix}\left(\dfrac{8}{3}-2x\right)^4=5^4.\\\left(\dfrac{8}{3}-2x\right)^4=\left(-5\right)^4.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{8}{3}-2x=5.\\\dfrac{8}{3}-2x=-5.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{7}{6}.\\x=\dfrac{23}{6}.\end{matrix}\right.\)

\(d,x^3=0,125.\\ \Leftrightarrow x^3=0,5^3.\\ \Rightarrow x=0,5.\)