1.

[tex](-2m^{2}k^{3})^{2}*(-3m^{3}k^{2})=4m^{4}k^{6}*(-3m^{3}k^{2})=-12m^{7}k^{8}[/tex]

2.

[tex]4(m-1)^{2}-3(1+m)(m-1)=4(m^{2}-2m+1)-3(m^{2}-1)=\\\\=4m^{2}-8m+4-3m^{2}+3=m^{2}-8m+7[/tex]

3.

[tex]\frac{x^{2}-xy}{y-1} *\frac{y-1}{x^{2}} +\frac{y-x}{2x} =\frac{x(x-y)}{y-1} *\frac{y-1}{x^{2}} +\frac{y-x}{2x}=\frac{x-y}{x} +\frac{y-x}{2x} =\frac{2x-2y}{2x} +\frac{y-x}{2x} =\frac{2x-2y+y-x}{2x} \\\\=\frac{x-y}{2x}[/tex]

4.

а)

[tex]2-3(x-2)=5-2x\\\\2-3x+6=5-2x\\\\8-3x=5-2x\\\\3x-2x=8-5\\\\x=3[/tex]

б)

[tex]\frac{x}{3} +\frac{x-1}{2} =4\\\\\frac{2x}{6} +\frac{3x-3}{6} =4\\\\\frac{2x+3x-3}{6} =4\\\\\frac{5x-3}{6} =4\\\\5x-3=24\\\\5x=27\\\\x=\frac{27}{5}=5\frac{2}{5} = 5.4[/tex]