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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-20}{13}-q)(2+q)& =(\color{red}{-q}+\color{orange}{\frac{-20}{13}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{-20}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qq-2q-\frac{20}{13}q-\frac{20}{13}.2& \text{Uitwerken } \\ & =-q^2+((-2)+(\frac{-20}{13}))q-\frac{40}{13} & \text{Neem samen} \\ &=-q^2-\frac{46}{13}q-\frac{40}{13} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-13}{6}+b)(x-\frac{18}{17})& =(\color{red}{b}+\color{orange}{\frac{-13}{6}}).(\color{green}{x}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{18}{17}b-\frac{13}{6}x+\frac{13}{6}.\frac{18}{17}& \text{Uitwerken } \\ & =bx-\frac{18}{17}b-\frac{13}{6}x+\frac{234}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{18}{17}b-\frac{13}{6}x+\frac{39}{17} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{4}{14}-q)(x-\frac{10}{17})& =(\color{red}{-q}+\color{orange}{\frac{2}{7}}).(\color{green}{x}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{10}{17}q+\frac{2}{7}x-\frac{2}{7}.\frac{10}{17}& \text{Uitwerken } \\ & =-qx+\frac{10}{17}q+\frac{2}{7}x-\frac{20}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-9}{6})(\frac{-3}{12}-b)& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{-b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{4}q-\frac{3}{2}b-\frac{3}{2}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq-\frac{1}{4}q-\frac{3}{2}b-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-14}{20}-q)(q+(-15))& =(\color{red}{-q}+\color{orange}{\frac{-7}{10}}).(\color{green}{q}+\color{blue}{(-15)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(-15)} + \color{orange}{(\frac{-7}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = -qq+15q-\frac{7}{10}q+\frac{7}{10}.15& \text{Uitwerken } \\ & =-q^2+(15+(\frac{-7}{10}))q+(\frac{-105}{10}) & \text{Neem samen} \\ &=-q^2+\frac{143}{10}q+(\frac{-105}{10}) & \text{Maak de som} \\ &=-q^2+\frac{143}{10}q+(\frac{-21}{2}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{2}-q)(\frac{6}{9}+x)& =(\color{red}{-q}+\color{orange}{\frac{7}{2}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{3}q+\frac{7}{2}x+\frac{7}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =-qx-\frac{2}{3}q+\frac{7}{2}x+\frac{14}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{2}{3}q+\frac{7}{2}x+\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{2}{8}-p)(b-\frac{19}{8})& =(\color{red}{-p}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{8}p+\frac{1}{4}b-\frac{1}{4}.\frac{19}{8}& \text{Uitwerken } \\ & =-bp+\frac{19}{8}p+\frac{1}{4}b-\frac{19}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{16}+p)(\frac{-14}{15}-b)& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{-b}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{14}{15}p-\frac{3}{4}b-\frac{3}{4}.\frac{14}{15}& \text{Uitwerken } \\ & =-bp-\frac{14}{15}p-\frac{3}{4}b-\frac{42}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{14}{15}p-\frac{3}{4}b-\frac{7}{10} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{15}{16}-x)(\frac{-16}{12}-p)& =(\color{red}{-x}+\color{orange}{\frac{15}{16}}).(\color{green}{-p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{15}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{4}{3}x-\frac{15}{16}p-\frac{15}{16}.\frac{4}{3}& \text{Uitwerken } \\ & =px+\frac{4}{3}x-\frac{15}{16}p-\frac{60}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{4}{3}x-\frac{15}{16}p-\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{8}{12})(a+\frac{-11}{20})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{20}b-\frac{2}{3}a+\frac{2}{3}.\frac{11}{20}& \text{Uitwerken } \\ & =ab-\frac{11}{20}b-\frac{2}{3}a+\frac{22}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{11}{20}b-\frac{2}{3}a+\frac{11}{30} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{18}{13}-x)(q-\frac{8}{9})& =(\color{red}{-x}+\color{orange}{\frac{18}{13}}).(\color{green}{q}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{18}{13})} . \color{green}{(q)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{8}{9}x+\frac{18}{13}q-\frac{18}{13}.\frac{8}{9}& \text{Uitwerken } \\ & =-qx+\frac{8}{9}x+\frac{18}{13}q-\frac{144}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{8}{9}x+\frac{18}{13}q-\frac{16}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-19}{10})(\frac{-16}{3}+q)& =(\color{red}{q}+\color{orange}{\frac{19}{10}}).(\color{green}{q}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{19}{10})} . \color{green}{(q)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{16}{3}q+\frac{19}{10}q-\frac{19}{10}.\frac{16}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-16}{3})+\frac{19}{10})q-(\frac{-304}{30}) & \text{Neem samen} \\ &=q^2-\frac{103}{30}q-(\frac{-304}{30}) & \text{Maak de som} \\ &=q^2-\frac{103}{30}q+\frac{152}{15} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-05 07:50:23
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