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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-8}{15})(x-\frac{-9}{5})& =(\color{red}{p}+\color{orange}{\frac{8}{15}}).(\color{green}{x}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{8}{15})} . \color{green}{(x)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{5}p+\frac{8}{15}x+\frac{8}{15}.\frac{9}{5}& \text{Uitwerken } \\ & =px+\frac{9}{5}p+\frac{8}{15}x+\frac{72}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{9}{5}p+\frac{8}{15}x+\frac{24}{25} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-6}{11}+b)(q+\frac{7}{11})& =(\color{red}{b}+\color{orange}{\frac{-6}{11}}).(\color{green}{q}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{11}b-\frac{6}{11}q-\frac{6}{11}.\frac{7}{11}& \text{Uitwerken } \\ & =bq+\frac{7}{11}b-\frac{6}{11}q-\frac{42}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{6}{17})(b-\frac{20}{2})& =(\color{red}{a}+\color{orange}{\frac{-6}{17}}).(\color{green}{b}+\color{blue}{(-10)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-10)} + \color{orange}{(\frac{-6}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = ab-10a-\frac{6}{17}b+\frac{6}{17}.10& \text{Uitwerken } \\ & =ab-10a-\frac{6}{17}b+\frac{60}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-11}{18}+p)(q-\frac{20}{9})& =(\color{red}{p}+\color{orange}{\frac{-11}{18}}).(\color{green}{q}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{20}{9}p-\frac{11}{18}q+\frac{11}{18}.\frac{20}{9}& \text{Uitwerken } \\ & =pq-\frac{20}{9}p-\frac{11}{18}q+\frac{220}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{20}{9}p-\frac{11}{18}q+\frac{110}{81} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-\frac{5}{3})(\frac{2}{10}-q)& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{-q}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{5}b+\frac{5}{3}q-\frac{5}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =-bq+\frac{1}{5}b+\frac{5}{3}q-\frac{5}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{1}{5}b+\frac{5}{3}q-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-2}{5}-b)(\frac{-13}{11}+a)& =(\color{red}{-b}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{13}{11}b-\frac{2}{5}a+\frac{2}{5}.\frac{13}{11}& \text{Uitwerken } \\ & =-ab+\frac{13}{11}b-\frac{2}{5}a+\frac{26}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{17}{10}+p)(p-\frac{-14}{10})& =(\color{red}{p}+\color{orange}{\frac{17}{10}}).(\color{green}{p}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{5}p+\frac{17}{10}p+\frac{17}{10}.\frac{7}{5}& \text{Uitwerken } \\ & =p^2+(\frac{7}{5}+\frac{17}{10})p+\frac{119}{50} & \text{Neem samen} \\ &=p^2+\frac{31}{10}p+\frac{119}{50} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-2}{4})(a+\frac{12}{8})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{2}b+\frac{1}{2}a+\frac{1}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =ab+\frac{3}{2}b+\frac{1}{2}a+\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{17}{6})(\frac{12}{4}-b)& =(\color{red}{a}+\color{orange}{\frac{17}{6}}).(\color{green}{-b}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{17}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -ab+3a-\frac{17}{6}b+\frac{17}{6}.3& \text{Uitwerken } \\ & =-ab+3a-\frac{17}{6}b+\frac{51}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+3a-\frac{17}{6}b+\frac{17}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-8}{19}+x)(\frac{-18}{13}+b)& =(\color{red}{x}+\color{orange}{\frac{-8}{19}}).(\color{green}{b}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{18}{13}x-\frac{8}{19}b+\frac{8}{19}.\frac{18}{13}& \text{Uitwerken } \\ & =bx-\frac{18}{13}x-\frac{8}{19}b+\frac{144}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{7}{16})(p-\frac{20}{6})& =(\color{red}{a}+\color{orange}{\frac{7}{16}}).(\color{green}{p}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{7}{16})} . \color{green}{(p)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{3}a+\frac{7}{16}p-\frac{7}{16}.\frac{10}{3}& \text{Uitwerken } \\ & =ap-\frac{10}{3}a+\frac{7}{16}p-\frac{70}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{10}{3}a+\frac{7}{16}p-\frac{35}{24} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-12}{20})(\frac{-6}{20}+x)& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{x}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{10}b+\frac{3}{5}x-\frac{3}{5}.\frac{3}{10}& \text{Uitwerken } \\ & =bx-\frac{3}{10}b+\frac{3}{5}x-\frac{9}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-29 11:37:46
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