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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{10}{10})(q+\frac{14}{7})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qx+2x+1q+1.2& \text{Uitwerken } \\ & =qx+2x+1q+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{6}{19}-x)(\frac{-6}{4}+a)& =(\color{red}{-x}+\color{orange}{\frac{6}{19}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{6}{19})} . \color{green}{(a)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{2}x+\frac{6}{19}a-\frac{6}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =-ax+\frac{3}{2}x+\frac{6}{19}a-\frac{18}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{3}{2}x+\frac{6}{19}a-\frac{9}{19} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{14}{11}+p)(x+\frac{-6}{8})& =(\color{red}{p}+\color{orange}{\frac{14}{11}}).(\color{green}{x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{14}{11})} . \color{green}{(x)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{4}p+\frac{14}{11}x-\frac{14}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =px-\frac{3}{4}p+\frac{14}{11}x-\frac{42}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{3}{4}p+\frac{14}{11}x-\frac{21}{22} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{12}{13}+p)(\frac{-1}{10}+p)& =(\color{red}{p}+\color{orange}{\frac{12}{13}}).(\color{green}{p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{12}{13})} . \color{green}{(p)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{10}p+\frac{12}{13}p-\frac{12}{13}.\frac{1}{10}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{10})+\frac{12}{13})p-(\frac{-12}{130}) & \text{Neem samen} \\ &=p^2+\frac{107}{130}p-(\frac{-12}{130}) & \text{Maak de som} \\ &=p^2+\frac{107}{130}p+\frac{6}{65} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{10}-x)(\frac{-2}{16}-x)& =(\color{red}{-x}+\color{orange}{\frac{-1}{5}}).(\color{green}{-x}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{8}x+\frac{1}{5}x+\frac{1}{5}.\frac{1}{8}& \text{Uitwerken } \\ & =x^2+(\frac{1}{8}+\frac{1}{5})x+\frac{1}{40} & \text{Neem samen} \\ &=x^2+\frac{13}{40}x+\frac{1}{40} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-13}{4})(b+\frac{11}{20})& =(\color{red}{a}+\color{orange}{\frac{-13}{4}}).(\color{green}{b}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{20}a-\frac{13}{4}b-\frac{13}{4}.\frac{11}{20}& \text{Uitwerken } \\ & =ab+\frac{11}{20}a-\frac{13}{4}b-\frac{143}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-19}{8}+q)(x+\frac{17}{8})& =(\color{red}{q}+\color{orange}{\frac{-19}{8}}).(\color{green}{x}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{-19}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{8}q-\frac{19}{8}x-\frac{19}{8}.\frac{17}{8}& \text{Uitwerken } \\ & =qx+\frac{17}{8}q-\frac{19}{8}x-\frac{323}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{14}{6})(q-\frac{11}{18})& =(\color{red}{p}+\color{orange}{\frac{7}{3}}).(\color{green}{q}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{18}p+\frac{7}{3}q-\frac{7}{3}.\frac{11}{18}& \text{Uitwerken } \\ & =pq-\frac{11}{18}p+\frac{7}{3}q-\frac{77}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-19}{14})(a-\frac{-5}{6})& =(\color{red}{b}+\color{orange}{\frac{19}{14}}).(\color{green}{a}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{19}{14})} . \color{green}{(a)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{6}b+\frac{19}{14}a+\frac{19}{14}.\frac{5}{6}& \text{Uitwerken } \\ & =ab+\frac{5}{6}b+\frac{19}{14}a+\frac{95}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{1}{2}+x)(\frac{3}{13}-q)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{-q}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{13}x-\frac{1}{2}q+\frac{1}{2}.\frac{3}{13}& \text{Uitwerken } \\ & =-qx+\frac{3}{13}x-\frac{1}{2}q+\frac{3}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{3}{15}-q)(a+\frac{-15}{7})& =(\color{red}{-q}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{15}{7}q+\frac{1}{5}a-\frac{1}{5}.\frac{15}{7}& \text{Uitwerken } \\ & =-aq+\frac{15}{7}q+\frac{1}{5}a-\frac{15}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{15}{7}q+\frac{1}{5}a-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{16}-x)(q+\frac{-11}{5})& =(\color{red}{-x}+\color{orange}{\frac{9}{16}}).(\color{green}{q}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(\frac{9}{16})} . \color{green}{(q)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{11}{5}x+\frac{9}{16}q-\frac{9}{16}.\frac{11}{5}& \text{Uitwerken } \\ & =-qx+\frac{11}{5}x+\frac{9}{16}q-\frac{99}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-02 20:44:09
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