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

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  1. \((q-\frac{11}{12})(\frac{-14}{17}-x)\)
  2. \((\frac{-4}{14}-a)(b+19)\)
  3. \((\frac{20}{14}-p)(q-\frac{-4}{13})\)
  4. \((q+\frac{-3}{2})(b-\frac{-11}{15})\)
  5. \((p-\frac{-4}{2})(a+\frac{3}{15})\)
  6. \((\frac{-1}{8}-p)(p+\frac{-4}{16})\)
  7. \((b+\frac{-7}{6})(q+\frac{19}{17})\)
  8. \((q-\frac{-8}{9})(x-\frac{8}{10})\)
  9. \((\frac{12}{14}+a)(p-\frac{-9}{20})\)
  10. \((\frac{-7}{16}-q)(q+\frac{18}{7})\)
  11. \((q-\frac{8}{5})(p-\frac{-3}{14})\)
  12. \((p-\frac{-16}{19})(\frac{-8}{4}-x)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{11}{12})(\frac{-14}{17}-x)& =(\color{red}{q}+\color{orange}{\frac{-11}{12}}).(\color{green}{-x}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{14}{17}q+\frac{11}{12}x+\frac{11}{12}.\frac{14}{17}& \text{Uitwerken } \\ & =-qx-\frac{14}{17}q+\frac{11}{12}x+\frac{154}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{14}{17}q+\frac{11}{12}x+\frac{77}{102} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-4}{14}-a)(b+19)& =(\color{red}{-a}+\color{orange}{\frac{-2}{7}}).(\color{green}{b}+\color{blue}{19})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(19)} + \color{orange}{(\frac{-2}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = -ab-19a-\frac{2}{7}b-\frac{2}{7}.19& \text{Uitwerken } \\ & =-ab-19a-\frac{2}{7}b-\frac{38}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{20}{14}-p)(q-\frac{-4}{13})& =(\color{red}{-p}+\color{orange}{\frac{10}{7}}).(\color{green}{q}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{10}{7})} . \color{green}{(q)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{13}p+\frac{10}{7}q+\frac{10}{7}.\frac{4}{13}& \text{Uitwerken } \\ & =-pq-\frac{4}{13}p+\frac{10}{7}q+\frac{40}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-3}{2})(b-\frac{-11}{15})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{b}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{15}q-\frac{3}{2}b-\frac{3}{2}.\frac{11}{15}& \text{Uitwerken } \\ & =bq+\frac{11}{15}q-\frac{3}{2}b-\frac{33}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{11}{15}q-\frac{3}{2}b-\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-4}{2})(a+\frac{3}{15})& =(\color{red}{p}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{5}p+2a+2.\frac{1}{5}& \text{Uitwerken } \\ & =ap+\frac{1}{5}p+2a+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-1}{8}-p)(p+\frac{-4}{16})& =(\color{red}{-p}+\color{orange}{\frac{-1}{8}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{1}{4}p-\frac{1}{8}p+\frac{1}{8}.\frac{1}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{1}{4}+(\frac{-1}{8}))p+(\frac{-1}{32}) & \text{Neem samen} \\ &=-p^2+\frac{1}{8}p+(\frac{-1}{32}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-7}{6})(q+\frac{19}{17})& =(\color{red}{b}+\color{orange}{\frac{-7}{6}}).(\color{green}{q}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{17}b-\frac{7}{6}q-\frac{7}{6}.\frac{19}{17}& \text{Uitwerken } \\ & =bq+\frac{19}{17}b-\frac{7}{6}q-\frac{133}{102} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-8}{9})(x-\frac{8}{10})& =(\color{red}{q}+\color{orange}{\frac{8}{9}}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{8}{9})} . \color{green}{(x)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{5}q+\frac{8}{9}x-\frac{8}{9}.\frac{4}{5}& \text{Uitwerken } \\ & =qx-\frac{4}{5}q+\frac{8}{9}x-\frac{32}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{12}{14}+a)(p-\frac{-9}{20})& =(\color{red}{a}+\color{orange}{\frac{6}{7}}).(\color{green}{p}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{6}{7})} . \color{green}{(p)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{20}a+\frac{6}{7}p+\frac{6}{7}.\frac{9}{20}& \text{Uitwerken } \\ & =ap+\frac{9}{20}a+\frac{6}{7}p+\frac{54}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{9}{20}a+\frac{6}{7}p+\frac{27}{70} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-7}{16}-q)(q+\frac{18}{7})& =(\color{red}{-q}+\color{orange}{\frac{-7}{16}}).(\color{green}{q}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{18}{7}q-\frac{7}{16}q-\frac{7}{16}.\frac{18}{7}& \text{Uitwerken } \\ & =-q^2+((\frac{-18}{7})+(\frac{-7}{16}))q-\frac{126}{112} & \text{Neem samen} \\ &=-q^2-\frac{337}{112}q-\frac{126}{112} & \text{Maak de som} \\ &=-q^2-\frac{337}{112}q-\frac{9}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(q-\frac{8}{5})(p-\frac{-3}{14})& =(\color{red}{q}+\color{orange}{\frac{-8}{5}}).(\color{green}{p}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{14}q-\frac{8}{5}p-\frac{8}{5}.\frac{3}{14}& \text{Uitwerken } \\ & =pq+\frac{3}{14}q-\frac{8}{5}p-\frac{24}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{3}{14}q-\frac{8}{5}p-\frac{12}{35} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-16}{19})(\frac{-8}{4}-x)& =(\color{red}{p}+\color{orange}{\frac{16}{19}}).(\color{green}{-x}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{16}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -px-2p-\frac{16}{19}x-\frac{16}{19}.2& \text{Uitwerken } \\ & =-px-2p-\frac{16}{19}x-\frac{32}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-26 13:57:39
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