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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{5}-q)(a+\frac{-17}{14})& =(\color{red}{-q}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{17}{14}q+3a-3.\frac{17}{14}& \text{Uitwerken } \\ & =-aq+\frac{17}{14}q+3a-\frac{51}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-16}{3}-a)(a+\frac{-4}{14})& =(\color{red}{-a}+\color{orange}{\frac{-16}{3}}).(\color{green}{a}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-16}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{2}{7}a-\frac{16}{3}a+\frac{16}{3}.\frac{2}{7}& \text{Uitwerken } \\ & =-a^2+(\frac{2}{7}+(\frac{-16}{3}))a+(\frac{-32}{21}) & \text{Neem samen} \\ &=-a^2-\frac{106}{21}a+(\frac{-32}{21}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-10}{8})(\frac{-14}{16}-p)& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{-p}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{7}{8}p+\frac{5}{4}p+\frac{5}{4}.\frac{7}{8}& \text{Uitwerken } \\ & =-p^2+((\frac{-7}{8})+\frac{5}{4})p+(\frac{-35}{32}) & \text{Neem samen} \\ &=-p^2+\frac{3}{8}p+(\frac{-35}{32}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a-\frac{2}{8})(p+\frac{18}{5})& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{18}{5}a-\frac{1}{4}p-\frac{1}{4}.\frac{18}{5}& \text{Uitwerken } \\ & =ap+\frac{18}{5}a-\frac{1}{4}p-\frac{18}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{18}{5}a-\frac{1}{4}p-\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-8}{19})(x-\frac{18}{14})& =(\color{red}{a}+\color{orange}{\frac{8}{19}}).(\color{green}{x}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{8}{19})} . \color{green}{(x)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{7}a+\frac{8}{19}x-\frac{8}{19}.\frac{9}{7}& \text{Uitwerken } \\ & =ax-\frac{9}{7}a+\frac{8}{19}x-\frac{72}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-15}{7}-p)(p+\frac{1}{3})& =(\color{red}{-p}+\color{orange}{\frac{-15}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{3}p-\frac{15}{7}p-\frac{15}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{3})+(\frac{-15}{7}))p-\frac{15}{21} & \text{Neem samen} \\ &=-p^2-\frac{52}{21}p-\frac{15}{21} & \text{Maak de som} \\ &=-p^2-\frac{52}{21}p-\frac{5}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{10}{16}+a)(x+\frac{11}{12})& =(\color{red}{a}+\color{orange}{\frac{5}{8}}).(\color{green}{x}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{12}a+\frac{5}{8}x+\frac{5}{8}.\frac{11}{12}& \text{Uitwerken } \\ & =ax+\frac{11}{12}a+\frac{5}{8}x+\frac{55}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{7}{4}-x)(\frac{-5}{3}-a)& =(\color{red}{-x}+\color{orange}{\frac{7}{4}}).(\color{green}{-a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{7}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{3}x-\frac{7}{4}a-\frac{7}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =ax+\frac{5}{3}x-\frac{7}{4}a-\frac{35}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-6}{16})(p-\frac{-20}{7})& =(\color{red}{q}+\color{orange}{\frac{3}{8}}).(\color{green}{p}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{3}{8})} . \color{green}{(p)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{20}{7}q+\frac{3}{8}p+\frac{3}{8}.\frac{20}{7}& \text{Uitwerken } \\ & =pq+\frac{20}{7}q+\frac{3}{8}p+\frac{60}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{20}{7}q+\frac{3}{8}p+\frac{15}{14} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-7}{5}-q)(\frac{1}{7}+x)& =(\color{red}{-q}+\color{orange}{\frac{-7}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{7}q-\frac{7}{5}x-\frac{7}{5}.\frac{1}{7}& \text{Uitwerken } \\ & =-qx-\frac{1}{7}q-\frac{7}{5}x-\frac{7}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{1}{7}q-\frac{7}{5}x-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-15}{14}+b)(q+\frac{-20}{11})& =(\color{red}{b}+\color{orange}{\frac{-15}{14}}).(\color{green}{q}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{20}{11}b-\frac{15}{14}q+\frac{15}{14}.\frac{20}{11}& \text{Uitwerken } \\ & =bq-\frac{20}{11}b-\frac{15}{14}q+\frac{300}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{20}{11}b-\frac{15}{14}q+\frac{150}{77} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-7}{11}-b)(\frac{16}{6}-a)& =(\color{red}{-b}+\color{orange}{\frac{-7}{11}}).(\color{green}{-a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{8}{3}b+\frac{7}{11}a-\frac{7}{11}.\frac{8}{3}& \text{Uitwerken } \\ & =ab-\frac{8}{3}b+\frac{7}{11}a-\frac{56}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-04 23:22:19
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