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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{6}{18})(b+\frac{-1}{7})& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{7}p-\frac{1}{3}b+\frac{1}{3}.\frac{1}{7}& \text{Uitwerken } \\ & =bp-\frac{1}{7}p-\frac{1}{3}b+\frac{1}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-4}{15}+a)(p+\frac{13}{13})& =(\color{red}{a}+\color{orange}{\frac{-4}{15}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-4}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1a-\frac{4}{15}p-\frac{4}{15}.1& \text{Uitwerken } \\ & =ap+1a-\frac{4}{15}p-\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-1}{19})(\frac{-2}{9}-q)& =(\color{red}{q}+\color{orange}{\frac{1}{19}}).(\color{green}{-q}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{1}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{2}{9}q-\frac{1}{19}q-\frac{1}{19}.\frac{2}{9}& \text{Uitwerken } \\ & =-q^2+((\frac{-2}{9})+(\frac{-1}{19}))q-\frac{2}{171} & \text{Neem samen} \\ &=-q^2-\frac{47}{171}q-\frac{2}{171} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-2}{6})(\frac{1}{19}-p)& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{-p}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{19}q+\frac{1}{3}p-\frac{1}{3}.\frac{1}{19}& \text{Uitwerken } \\ & =-pq+\frac{1}{19}q+\frac{1}{3}p-\frac{1}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{16}{14})(q+\frac{7}{20})& =(\color{red}{b}+\color{orange}{\frac{8}{7}}).(\color{green}{q}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{20}b+\frac{8}{7}q+\frac{8}{7}.\frac{7}{20}& \text{Uitwerken } \\ & =bq+\frac{7}{20}b+\frac{8}{7}q+\frac{56}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{7}{20}b+\frac{8}{7}q+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-4}{4})(\frac{2}{14}-b)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{7}a+1b-1.\frac{1}{7}& \text{Uitwerken } \\ & =-ab+\frac{1}{7}a+1b-\frac{1}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-15}{7}+q)(p+\frac{-11}{16})& =(\color{red}{q}+\color{orange}{\frac{-15}{7}}).(\color{green}{p}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{16}q-\frac{15}{7}p+\frac{15}{7}.\frac{11}{16}& \text{Uitwerken } \\ & =pq-\frac{11}{16}q-\frac{15}{7}p+\frac{165}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-18}{14})(\frac{-17}{6}-a)& =(\color{red}{a}+\color{orange}{\frac{-9}{7}}).(\color{green}{-a}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{17}{6}a+\frac{9}{7}a+\frac{9}{7}.\frac{17}{6}& \text{Uitwerken } \\ & =-a^2+((\frac{-17}{6})+\frac{9}{7})a+(\frac{-153}{42}) & \text{Neem samen} \\ &=-a^2-\frac{65}{42}a+(\frac{-153}{42}) & \text{Maak de som} \\ &=-a^2-\frac{65}{42}a+(\frac{-51}{14}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{7}{8}-p)(a-\frac{-16}{11})& =(\color{red}{-p}+\color{orange}{\frac{7}{8}}).(\color{green}{a}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{16}{11}p+\frac{7}{8}a+\frac{7}{8}.\frac{16}{11}& \text{Uitwerken } \\ & =-ap-\frac{16}{11}p+\frac{7}{8}a+\frac{112}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{16}{11}p+\frac{7}{8}a+\frac{14}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-15}{6}+q)(a+\frac{-12}{4})& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = aq-3q-\frac{5}{2}a+\frac{5}{2}.3& \text{Uitwerken } \\ & =aq-3q-\frac{5}{2}a+\frac{15}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-8}{6}-a)(a-\frac{13}{17})& =(\color{red}{-a}+\color{orange}{\frac{-4}{3}}).(\color{green}{a}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{13}{17}a-\frac{4}{3}a+\frac{4}{3}.\frac{13}{17}& \text{Uitwerken } \\ & =-a^2+(\frac{13}{17}+(\frac{-4}{3}))a+(\frac{-52}{51}) & \text{Neem samen} \\ &=-a^2-\frac{29}{51}a+(\frac{-52}{51}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-9}{13})(x+\frac{-6}{3})& =(\color{red}{q}+\color{orange}{\frac{-9}{13}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-9}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2q-\frac{9}{13}x+\frac{9}{13}.2& \text{Uitwerken } \\ & =qx-2q-\frac{9}{13}x+\frac{18}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-07 13:54:07
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