$a)\left(\frac{1}{2}a+\frac{1}{3}\right)\left(\frac{6}{7}a+12\right)=$   $\frac{1}{2}a\left(\frac{6}{7}a+12\right)+\frac{1}{3}\left(\frac{6}{7}a+12\right)=$  

$=\frac{3}{7}{a}^2+6a+\frac{2}{7}a+4=$   $\frac{3}{7}{a}^2+6\frac{2}{7}a+4$  

 

$b)\left(6x-12\right)\left(\frac{2}{3}{x}^2+1\frac{5}{6}x-2\right)=$   $6\cdot \left(x-2\right)\left(\frac{2}{3}{x}^2+\frac{11}{6}x-2\right)=$  

$=\left(x-2\right)\cdot 6\cdot \left(\frac{2}{3}{x}^2+\frac{11}{6}x-2\right)=$   $\left(x-2\right)\left(4x^2+11x-2\right)=$  

$=x\left(4x^2+11x-12\right)-2\left(4x^2+11x-2\right)=$   

$=4x^3+11x^2-12x-8x^2-22x+4=$   

$=4x^3+3x^2-34x+4$   

 

$c)\left(1\frac{1}{4}{x}^2+4\frac{1}{2}x-3\right)\left(8-20x\right)=$   $\left(\frac{5}{4}{x}^2+\frac{9}{2}x-3\right)\cdot 4\cdot \left(2-5x\right)=$  

$=\left(5x^2+18x-12\right)\cdot \left(2-5x\right)=$   

$=\left(5x^2+18x-12\right)\cdot 2+\left(5x^2+18x-12\right)\cdot \left(-5x\right)=$  

$=10x^2+36x-24-25x^3-90x^2+60x=$  

$=-25x^3-80x^2+96x-24$  

 

$d)\left(0,25m+0,8\right)\left(0,4m-0,75\right)=$   $\left(\frac{1}{4}m+\frac{4}{5}\right)\left(\frac{2}{5}m-\frac{3}{4}\right)=$   

$=\frac{1}{4}m\left(\frac{2}{5}m-\frac{3}{4}\right)+\frac{4}{5}\left(\frac{2}{5}m-\frac{3}{4}\right)=$  

$=\frac{2}{20}{m}^2-\frac{3}{16}m+\frac{8}{25}m-\frac{3}{5}=$  

$=\frac{1}{10}{m}^2-\frac{75}{400}m+\frac{128}{400}m-\frac{3}{5}=$  

$=\frac{1}{110}{m}^2+\frac{53}{400}m-\frac{3}{5}$