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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{18}{2}-a)(b+\frac{19}{5})& =(\color{red}{-a}+\color{orange}{9}).(\color{green}{b}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(9)} . \color{green}{(b)} + \color{orange}{(9)} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{19}{5}a+9b+9.\frac{19}{5}& \text{Uitwerken } \\ & =-ab-\frac{19}{5}a+9b+\frac{171}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-20}{15})(p-\frac{-12}{13})& =(\color{red}{a}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{12}{13}a+\frac{4}{3}p+\frac{4}{3}.\frac{12}{13}& \text{Uitwerken } \\ & =ap+\frac{12}{13}a+\frac{4}{3}p+\frac{48}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{12}{13}a+\frac{4}{3}p+\frac{16}{13} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{3}{15}-q)(q+\frac{6}{18})& =(\color{red}{-q}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{3}q+\frac{1}{5}q+\frac{1}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{3})+\frac{1}{5})q+(\frac{-1}{15}) & \text{Neem samen} \\ &=-q^2-\frac{2}{15}q+(\frac{-1}{15}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-20}{9})(x+\frac{-16}{9})& =(\color{red}{q}+\color{orange}{\frac{-20}{9}}).(\color{green}{x}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-20}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{9}q-\frac{20}{9}x+\frac{20}{9}.\frac{16}{9}& \text{Uitwerken } \\ & =qx-\frac{16}{9}q-\frac{20}{9}x+\frac{320}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{10}{12})(\frac{-16}{6}-q)& =(\color{red}{q}+\color{orange}{\frac{5}{6}}).(\color{green}{-q}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{8}{3}q-\frac{5}{6}q-\frac{5}{6}.\frac{8}{3}& \text{Uitwerken } \\ & =-q^2+((\frac{-8}{3})+(\frac{-5}{6}))q-\frac{40}{18} & \text{Neem samen} \\ &=-q^2-\frac{21}{6}q-\frac{40}{18} & \text{Maak de som} \\ &=-q^2-\frac{7}{2}q-\frac{20}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{19}{7}-p)(p-\frac{-3}{12})& =(\color{red}{-p}+\color{orange}{\frac{19}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{19}{7})} . \color{green}{(p)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{4}p+\frac{19}{7}p+\frac{19}{7}.\frac{1}{4}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{4})+\frac{19}{7})p+(\frac{-19}{28}) & \text{Neem samen} \\ &=-p^2+\frac{69}{28}p+(\frac{-19}{28}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-14}{11})(x-\frac{5}{19})& =(\color{red}{q}+\color{orange}{\frac{-14}{11}}).(\color{green}{x}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{19}q-\frac{14}{11}x+\frac{14}{11}.\frac{5}{19}& \text{Uitwerken } \\ & =qx-\frac{5}{19}q-\frac{14}{11}x+\frac{70}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-13}{6})(\frac{-10}{13}+q)& =(\color{red}{p}+\color{orange}{\frac{-13}{6}}).(\color{green}{q}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{13}p-\frac{13}{6}q+\frac{13}{6}.\frac{10}{13}& \text{Uitwerken } \\ & =pq-\frac{10}{13}p-\frac{13}{6}q+\frac{130}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{10}{13}p-\frac{13}{6}q+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-6}{11})(\frac{-7}{10}-q)& =(\color{red}{a}+\color{orange}{\frac{-6}{11}}).(\color{green}{-q}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{7}{10}a+\frac{6}{11}q+\frac{6}{11}.\frac{7}{10}& \text{Uitwerken } \\ & =-aq-\frac{7}{10}a+\frac{6}{11}q+\frac{42}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{7}{10}a+\frac{6}{11}q+\frac{21}{55} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-2}{15}-b)(\frac{-19}{9}-a)& =(\color{red}{-b}+\color{orange}{\frac{-2}{15}}).(\color{green}{-a}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{9}b+\frac{2}{15}a+\frac{2}{15}.\frac{19}{9}& \text{Uitwerken } \\ & =ab+\frac{19}{9}b+\frac{2}{15}a+\frac{38}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-11}{19}+a)(a+\frac{12}{9})& =(\color{red}{a}+\color{orange}{\frac{-11}{19}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{3}a-\frac{11}{19}a-\frac{11}{19}.\frac{4}{3}& \text{Uitwerken } \\ & =a^2+(\frac{4}{3}+(\frac{-11}{19}))a-(\frac{-44}{57}) & \text{Neem samen} \\ &=a^2+\frac{43}{57}a-(\frac{-44}{57}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{13}+q)(x+\frac{7}{17})& =(\color{red}{q}+\color{orange}{\frac{-15}{13}}).(\color{green}{x}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{17}q-\frac{15}{13}x-\frac{15}{13}.\frac{7}{17}& \text{Uitwerken } \\ & =qx+\frac{7}{17}q-\frac{15}{13}x-\frac{105}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-14 19:43:22
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