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

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  1. \((q-\frac{-11}{9})(a-\frac{-14}{3})\)
  2. \((q-\frac{2}{20})(a-\frac{-1}{10})\)
  3. \((x-\frac{-12}{13})(a-\frac{-12}{10})\)
  4. \((p-\frac{-12}{2})(a+\frac{12}{18})\)
  5. \((\frac{-1}{11}+p)(a-\frac{15}{19})\)
  6. \((\frac{1}{20}+a)(\frac{-8}{19}-p)\)
  7. \((x-\frac{-7}{9})(\frac{-19}{18}+a)\)
  8. \((q-\frac{-7}{16})(13+a)\)
  9. \((\frac{9}{12}-a)(b+\frac{20}{12})\)
  10. \((\frac{-13}{19}-p)(a-\frac{18}{12})\)
  11. \((a+\frac{8}{15})(\frac{-10}{12}-x)\)
  12. \((\frac{14}{7}-p)(q+\frac{-5}{8})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-11}{9})(a-\frac{-14}{3})& =(\color{red}{q}+\color{orange}{\frac{11}{9}}).(\color{green}{a}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{11}{9})} . \color{green}{(a)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{14}{3}q+\frac{11}{9}a+\frac{11}{9}.\frac{14}{3}& \text{Uitwerken } \\ & =aq+\frac{14}{3}q+\frac{11}{9}a+\frac{154}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{2}{20})(a-\frac{-1}{10})& =(\color{red}{q}+\color{orange}{\frac{-1}{10}}).(\color{green}{a}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{10}q-\frac{1}{10}a-\frac{1}{10}.\frac{1}{10}& \text{Uitwerken } \\ & =aq+\frac{1}{10}q-\frac{1}{10}a-\frac{1}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-12}{13})(a-\frac{-12}{10})& =(\color{red}{x}+\color{orange}{\frac{12}{13}}).(\color{green}{a}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{12}{13})} . \color{green}{(a)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{5}x+\frac{12}{13}a+\frac{12}{13}.\frac{6}{5}& \text{Uitwerken } \\ & =ax+\frac{6}{5}x+\frac{12}{13}a+\frac{72}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-12}{2})(a+\frac{12}{18})& =(\color{red}{p}+\color{orange}{6}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(6)} . \color{green}{(a)} + \color{orange}{(6)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{3}p+6a+6.\frac{2}{3}& \text{Uitwerken } \\ & =ap+\frac{2}{3}p+6a+\frac{12}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{2}{3}p+6a+4 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-1}{11}+p)(a-\frac{15}{19})& =(\color{red}{p}+\color{orange}{\frac{-1}{11}}).(\color{green}{a}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{19}p-\frac{1}{11}a+\frac{1}{11}.\frac{15}{19}& \text{Uitwerken } \\ & =ap-\frac{15}{19}p-\frac{1}{11}a+\frac{15}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{20}+a)(\frac{-8}{19}-p)& =(\color{red}{a}+\color{orange}{\frac{1}{20}}).(\color{green}{-p}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{1}{20})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{8}{19}a-\frac{1}{20}p-\frac{1}{20}.\frac{8}{19}& \text{Uitwerken } \\ & =-ap-\frac{8}{19}a-\frac{1}{20}p-\frac{8}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{8}{19}a-\frac{1}{20}p-\frac{2}{95} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-7}{9})(\frac{-19}{18}+a)& =(\color{red}{x}+\color{orange}{\frac{7}{9}}).(\color{green}{a}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{7}{9})} . \color{green}{(a)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{18}x+\frac{7}{9}a-\frac{7}{9}.\frac{19}{18}& \text{Uitwerken } \\ & =ax-\frac{19}{18}x+\frac{7}{9}a-\frac{133}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-7}{16})(13+a)& =(\color{red}{q}+\color{orange}{\frac{7}{16}}).(\color{green}{a}+\color{blue}{13})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(13)} + \color{orange}{(\frac{7}{16})} . \color{green}{(a)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = aq+13q+\frac{7}{16}a+\frac{7}{16}.13& \text{Uitwerken } \\ & =aq+13q+\frac{7}{16}a+\frac{91}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{9}{12}-a)(b+\frac{20}{12})& =(\color{red}{-a}+\color{orange}{\frac{3}{4}}).(\color{green}{b}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{5}{3}a+\frac{3}{4}b+\frac{3}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =-ab-\frac{5}{3}a+\frac{3}{4}b+\frac{15}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{5}{3}a+\frac{3}{4}b+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-13}{19}-p)(a-\frac{18}{12})& =(\color{red}{-p}+\color{orange}{\frac{-13}{19}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{2}p-\frac{13}{19}a+\frac{13}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =-ap+\frac{3}{2}p-\frac{13}{19}a+\frac{39}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{8}{15})(\frac{-10}{12}-x)& =(\color{red}{a}+\color{orange}{\frac{8}{15}}).(\color{green}{-x}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{8}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{6}a-\frac{8}{15}x-\frac{8}{15}.\frac{5}{6}& \text{Uitwerken } \\ & =-ax-\frac{5}{6}a-\frac{8}{15}x-\frac{40}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{5}{6}a-\frac{8}{15}x-\frac{4}{9} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{14}{7}-p)(q+\frac{-5}{8})& =(\color{red}{-p}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{8}p+2q-2.\frac{5}{8}& \text{Uitwerken } \\ & =-pq+\frac{5}{8}p+2q-\frac{10}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{5}{8}p+2q-\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
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