Distributiviteit \((a+r)(b+s)\)

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1. \((\frac{-2}{10}+b)(x+\frac{19}{12})\)
2. \((x-\frac{-20}{20})(b+\frac{-15}{6})\)
3. \((\frac{18}{4}+a)(\frac{6}{5}+x)\)
4. \((\frac{-2}{13}-b)(\frac{-15}{15}-p)\)
5. \((\frac{14}{19}-p)(\frac{9}{11}+b)\)
6. \((\frac{1}{6}-x)(\frac{4}{17}-q)\)
7. \((\frac{13}{12}-p)(p-\frac{1}{14})\)
8. \((p-\frac{-1}{18})(\frac{11}{9}+p)\)
9. \((q+\frac{-19}{2})(\frac{20}{2}-b)\)
10. \((x-\frac{7}{14})(\frac{-12}{8}+a)\)
11. \((a+(-13))(\frac{-10}{4}-a)\)
12. \((q-\frac{7}{12})(p-\frac{-4}{20})\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-2}{10}+b)(x+\frac{19}{12})& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{x}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{12}b-\frac{1}{5}x-\frac{1}{5}.\frac{19}{12}& \text{Uitwerken } \\ & =bx+\frac{19}{12}b-\frac{1}{5}x-\frac{19}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-\frac{-20}{20})(b+\frac{-15}{6})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{2}x+1b-1.\frac{5}{2}& \text{Uitwerken } \\ & =bx-\frac{5}{2}x+1b-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{18}{4}+a)(\frac{6}{5}+x)& =(\color{red}{a}+\color{orange}{\frac{9}{2}}).(\color{green}{x}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{5}a+\frac{9}{2}x+\frac{9}{2}.\frac{6}{5}& \text{Uitwerken } \\ & =ax+\frac{6}{5}a+\frac{9}{2}x+\frac{54}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{6}{5}a+\frac{9}{2}x+\frac{27}{5} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-2}{13}-b)(\frac{-15}{15}-p)& =(\color{red}{-b}+\color{orange}{\frac{-2}{13}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp+1b+\frac{2}{13}p+\frac{2}{13}.1& \text{Uitwerken } \\ & =bp+1b+\frac{2}{13}p+\frac{2}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{14}{19}-p)(\frac{9}{11}+b)& =(\color{red}{-p}+\color{orange}{\frac{14}{19}}).(\color{green}{b}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{14}{19})} . \color{green}{(b)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{9}{11}p+\frac{14}{19}b+\frac{14}{19}.\frac{9}{11}& \text{Uitwerken } \\ & =-bp-\frac{9}{11}p+\frac{14}{19}b+\frac{126}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{1}{6}-x)(\frac{4}{17}-q)& =(\color{red}{-x}+\color{orange}{\frac{1}{6}}).(\color{green}{-q}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{1}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{17}x-\frac{1}{6}q+\frac{1}{6}.\frac{4}{17}& \text{Uitwerken } \\ & =qx-\frac{4}{17}x-\frac{1}{6}q+\frac{4}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{4}{17}x-\frac{1}{6}q+\frac{2}{51} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{13}{12}-p)(p-\frac{1}{14})& =(\color{red}{-p}+\color{orange}{\frac{13}{12}}).(\color{green}{p}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{13}{12})} . \color{green}{(p)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{1}{14}p+\frac{13}{12}p-\frac{13}{12}.\frac{1}{14}& \text{Uitwerken } \\ & =-p^2+(\frac{1}{14}+\frac{13}{12})p-\frac{13}{168} & \text{Neem samen} \\ &=-p^2+\frac{97}{84}p-\frac{13}{168} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(p-\frac{-1}{18})(\frac{11}{9}+p)& =(\color{red}{p}+\color{orange}{\frac{1}{18}}).(\color{green}{p}+\color{blue}{\frac{11}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{11}{9})} + \color{orange}{(\frac{1}{18})} . \color{green}{(p)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{11}{9})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{11}{9}p+\frac{1}{18}p+\frac{1}{18}.\frac{11}{9}& \text{Uitwerken } \\ & =p^2+(\frac{11}{9}+\frac{1}{18})p+\frac{11}{162} & \text{Neem samen} \\ &=p^2+\frac{23}{18}p+\frac{11}{162} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(q+\frac{-19}{2})(\frac{20}{2}-b)& =(\color{red}{q}+\color{orange}{\frac{-19}{2}}).(\color{green}{-b}+\color{blue}{10})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(10)} + \color{orange}{(\frac{-19}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -bq+10q+\frac{19}{2}b-\frac{19}{2}.10& \text{Uitwerken } \\ & =-bq+10q+\frac{19}{2}b-\frac{190}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+10q+\frac{19}{2}b-95 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(x-\frac{7}{14})(\frac{-12}{8}+a)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{2}x-\frac{1}{2}a+\frac{1}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =ax-\frac{3}{2}x-\frac{1}{2}a+\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+(-13))(\frac{-10}{4}-a)& =(\color{red}{a}+\color{orange}{(-13)}).(\color{green}{-a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(-13)} . \color{green}{(-a)} + \color{orange}{(-13)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{2}a+13a+13.\frac{5}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{2})+13)a+(\frac{-65}{2}) & \text{Neem samen} \\ &=-a^2+\frac{21}{2}a+(\frac{-65}{2}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(q-\frac{7}{12})(p-\frac{-4}{20})& =(\color{red}{q}+\color{orange}{\frac{-7}{12}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{5}q-\frac{7}{12}p-\frac{7}{12}.\frac{1}{5}& \text{Uitwerken } \\ & =pq+\frac{1}{5}q-\frac{7}{12}p-\frac{7}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)