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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{19}{19})(p-\frac{-20}{2})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{p}+\color{blue}{10})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(10)} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = ap+10a+1p+1.10& \text{Uitwerken } \\ & =ap+10a+1p+10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-14}{12})(\frac{17}{6}-q)& =(\color{red}{b}+\color{orange}{\frac{-7}{6}}).(\color{green}{-q}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{17}{6}b+\frac{7}{6}q-\frac{7}{6}.\frac{17}{6}& \text{Uitwerken } \\ & =-bq+\frac{17}{6}b+\frac{7}{6}q-\frac{119}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-4}{16})(a-\frac{3}{15})& =(\color{red}{q}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{5}q+\frac{1}{4}a-\frac{1}{4}.\frac{1}{5}& \text{Uitwerken } \\ & =aq-\frac{1}{5}q+\frac{1}{4}a-\frac{1}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{3}{6}-a)(x-\frac{17}{10})& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{10}a+\frac{1}{2}x-\frac{1}{2}.\frac{17}{10}& \text{Uitwerken } \\ & =-ax+\frac{17}{10}a+\frac{1}{2}x-\frac{17}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{6}{3}+q)(b-\frac{11}{4})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{4}q+2b-2.\frac{11}{4}& \text{Uitwerken } \\ & =bq-\frac{11}{4}q+2b-\frac{22}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{11}{4}q+2b-\frac{11}{2} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-19}{12}-a)(\frac{-1}{13}-b)& =(\color{red}{-a}+\color{orange}{\frac{-19}{12}}).(\color{green}{-b}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{13}a+\frac{19}{12}b+\frac{19}{12}.\frac{1}{13}& \text{Uitwerken } \\ & =ab+\frac{1}{13}a+\frac{19}{12}b+\frac{19}{156} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{15}{19}+b)(\frac{3}{7}-a)& =(\color{red}{b}+\color{orange}{\frac{15}{19}}).(\color{green}{-a}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{15}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{7}b-\frac{15}{19}a+\frac{15}{19}.\frac{3}{7}& \text{Uitwerken } \\ & =-ab+\frac{3}{7}b-\frac{15}{19}a+\frac{45}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-8}{13})(\frac{-7}{13}-p)& =(\color{red}{x}+\color{orange}{\frac{8}{13}}).(\color{green}{-p}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{8}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{13}x-\frac{8}{13}p-\frac{8}{13}.\frac{7}{13}& \text{Uitwerken } \\ & =-px-\frac{7}{13}x-\frac{8}{13}p-\frac{56}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{11}{5})(14+q)& =(\color{red}{b}+\color{orange}{\frac{-11}{5}}).(\color{green}{q}+\color{blue}{14})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(14)} + \color{orange}{(\frac{-11}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = bq+14b-\frac{11}{5}q-\frac{11}{5}.14& \text{Uitwerken } \\ & =bq+14b-\frac{11}{5}q-\frac{154}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{-12}{13})(x+\frac{-6}{6})& =(\color{red}{x}+\color{orange}{\frac{-12}{13}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-12}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = xx-1x-\frac{12}{13}x+\frac{12}{13}.1& \text{Uitwerken } \\ & =x^2+((-1)+(\frac{-12}{13}))x+\frac{12}{13} & \text{Neem samen} \\ &=x^2-\frac{25}{13}x+\frac{12}{13} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{20}+q)(\frac{-5}{5}-x)& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx-1q-\frac{1}{5}x-\frac{1}{5}.1& \text{Uitwerken } \\ & =-qx-1q-\frac{1}{5}x-\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{14}{7}+x)(\frac{16}{18}+a)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{9}x+2a+2.\frac{8}{9}& \text{Uitwerken } \\ & =ax+\frac{8}{9}x+2a+\frac{16}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-13 22:12:47
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