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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-14}{13})(x-\frac{-6}{7})& =(\color{red}{a}+\color{orange}{\frac{-14}{13}}).(\color{green}{x}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{7}a-\frac{14}{13}x-\frac{14}{13}.\frac{6}{7}& \text{Uitwerken } \\ & =ax+\frac{6}{7}a-\frac{14}{13}x-\frac{84}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{6}{7}a-\frac{14}{13}x-\frac{12}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x+\frac{-6}{10})(b+\frac{-7}{5})& =(\color{red}{x}+\color{orange}{\frac{-3}{5}}).(\color{green}{b}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{5}x-\frac{3}{5}b+\frac{3}{5}.\frac{7}{5}& \text{Uitwerken } \\ & =bx-\frac{7}{5}x-\frac{3}{5}b+\frac{21}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{11}{11})(\frac{9}{20}+p)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{20}q+1p+1.\frac{9}{20}& \text{Uitwerken } \\ & =pq+\frac{9}{20}q+1p+\frac{9}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{13}{19}+x)(\frac{16}{14}-x)& =(\color{red}{x}+\color{orange}{\frac{13}{19}}).(\color{green}{-x}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{13}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{8}{7}x-\frac{13}{19}x+\frac{13}{19}.\frac{8}{7}& \text{Uitwerken } \\ & =-x^2+(\frac{8}{7}+(\frac{-13}{19}))x+(\frac{-104}{133}) & \text{Neem samen} \\ &=-x^2+\frac{61}{133}x+(\frac{-104}{133}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{6}+x)(p-\frac{-13}{11})& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{11}x+\frac{3}{2}p+\frac{3}{2}.\frac{13}{11}& \text{Uitwerken } \\ & =px+\frac{13}{11}x+\frac{3}{2}p+\frac{39}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-16}{2}-p)(x-\frac{15}{17})& =(\color{red}{-p}+\color{orange}{(-8)}).(\color{green}{x}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(-8)} . \color{green}{(x)} + \color{orange}{(-8)} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{15}{17}p-8x+8.\frac{15}{17}& \text{Uitwerken } \\ & =-px+\frac{15}{17}p-8x+\frac{120}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{15}{12}-p)(\frac{16}{19}-b)& =(\color{red}{-p}+\color{orange}{\frac{5}{4}}).(\color{green}{-b}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{16}{19}p-\frac{5}{4}b+\frac{5}{4}.\frac{16}{19}& \text{Uitwerken } \\ & =bp-\frac{16}{19}p-\frac{5}{4}b+\frac{80}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{16}{19}p-\frac{5}{4}b+\frac{20}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-9}{4})(p-\frac{-4}{9})& =(\color{red}{b}+\color{orange}{\frac{-9}{4}}).(\color{green}{p}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{9}b-\frac{9}{4}p-\frac{9}{4}.\frac{4}{9}& \text{Uitwerken } \\ & =bp+\frac{4}{9}b-\frac{9}{4}p-\frac{36}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{4}{9}b-\frac{9}{4}p-1 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-2}{7}+p)(\frac{6}{14}-p)& =(\color{red}{p}+\color{orange}{\frac{-2}{7}}).(\color{green}{-p}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{3}{7}p+\frac{2}{7}p-\frac{2}{7}.\frac{3}{7}& \text{Uitwerken } \\ & =-p^2+(\frac{3}{7}+\frac{2}{7})p-\frac{6}{49} & \text{Neem samen} \\ &=-p^2+\frac{5}{7}p-\frac{6}{49} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{12}-q)(a+\frac{-4}{11})& =(\color{red}{-q}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{4}{11}q+\frac{3}{2}a-\frac{3}{2}.\frac{4}{11}& \text{Uitwerken } \\ & =-aq+\frac{4}{11}q+\frac{3}{2}a-\frac{12}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{4}{11}q+\frac{3}{2}a-\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q-\frac{19}{7})(x+\frac{10}{14})& =(\color{red}{q}+\color{orange}{\frac{-19}{7}}).(\color{green}{x}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{7}q-\frac{19}{7}x-\frac{19}{7}.\frac{5}{7}& \text{Uitwerken } \\ & =qx+\frac{5}{7}q-\frac{19}{7}x-\frac{95}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{9}+q)(\frac{-13}{5}+b)& =(\color{red}{q}+\color{orange}{\frac{8}{9}}).(\color{green}{b}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{8}{9})} . \color{green}{(b)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{5}q+\frac{8}{9}b-\frac{8}{9}.\frac{13}{5}& \text{Uitwerken } \\ & =bq-\frac{13}{5}q+\frac{8}{9}b-\frac{104}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-14 05:07:41
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