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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{11}{4})(\frac{-14}{18}+q)& =(\color{red}{q}+\color{orange}{\frac{11}{4}}).(\color{green}{q}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{11}{4})} . \color{green}{(q)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{9}q+\frac{11}{4}q-\frac{11}{4}.\frac{7}{9}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{9})+\frac{11}{4})q-(\frac{-77}{36}) & \text{Neem samen} \\ &=q^2+\frac{71}{36}q-(\frac{-77}{36}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-11}{8}-b)(\frac{-20}{19}+q)& =(\color{red}{-b}+\color{orange}{\frac{-11}{8}}).(\color{green}{q}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{20}{19}b-\frac{11}{8}q+\frac{11}{8}.\frac{20}{19}& \text{Uitwerken } \\ & =-bq+\frac{20}{19}b-\frac{11}{8}q+\frac{220}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{20}{19}b-\frac{11}{8}q+\frac{55}{38} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{18}{2}-p)(p-\frac{-8}{17})& =(\color{red}{-p}+\color{orange}{9}).(\color{green}{p}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(9)} . \color{green}{(p)} + \color{orange}{(9)} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{8}{17}p+9p+9.\frac{8}{17}& \text{Uitwerken } \\ & =-p^2+((\frac{-8}{17})+9)p+(\frac{-72}{17}) & \text{Neem samen} \\ &=-p^2+\frac{145}{17}p+(\frac{-72}{17}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-10}{3}-b)(x-\frac{-14}{16})& =(\color{red}{-b}+\color{orange}{\frac{-10}{3}}).(\color{green}{x}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{7}{8}b-\frac{10}{3}x-\frac{10}{3}.\frac{7}{8}& \text{Uitwerken } \\ & =-bx-\frac{7}{8}b-\frac{10}{3}x-\frac{70}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{7}{8}b-\frac{10}{3}x-\frac{35}{12} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-1}{12})(q-\frac{-10}{18})& =(\color{red}{p}+\color{orange}{\frac{1}{12}}).(\color{green}{q}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{1}{12})} . \color{green}{(q)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{9}p+\frac{1}{12}q+\frac{1}{12}.\frac{5}{9}& \text{Uitwerken } \\ & =pq+\frac{5}{9}p+\frac{1}{12}q+\frac{5}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-19}{13}-p)(\frac{8}{11}-q)& =(\color{red}{-p}+\color{orange}{\frac{-19}{13}}).(\color{green}{-q}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{11}p+\frac{19}{13}q-\frac{19}{13}.\frac{8}{11}& \text{Uitwerken } \\ & =pq-\frac{8}{11}p+\frac{19}{13}q-\frac{152}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-10}{20}-a)(x-\frac{12}{3})& =(\color{red}{-a}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ax+4a-\frac{1}{2}x+\frac{1}{2}.4& \text{Uitwerken } \\ & =-ax+4a-\frac{1}{2}x+\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+4a-\frac{1}{2}x+2 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-4}{18}+q)(\frac{4}{20}-x)& =(\color{red}{q}+\color{orange}{\frac{-2}{9}}).(\color{green}{-x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{5}q+\frac{2}{9}x-\frac{2}{9}.\frac{1}{5}& \text{Uitwerken } \\ & =-qx+\frac{1}{5}q+\frac{2}{9}x-\frac{2}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-20}{6}+x)(\frac{-18}{10}+x)& =(\color{red}{x}+\color{orange}{\frac{-10}{3}}).(\color{green}{x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{9}{5}x-\frac{10}{3}x+\frac{10}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-9}{5})+(\frac{-10}{3}))x+\frac{90}{15} & \text{Neem samen} \\ &=x^2-\frac{77}{15}x+\frac{90}{15} & \text{Maak de som} \\ &=x^2-\frac{77}{15}x+6 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-10}{3})((-19)+b)& =(\color{red}{q}+\color{orange}{\frac{-10}{3}}).(\color{green}{b}+\color{blue}{(-19)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-19)} + \color{orange}{(\frac{-10}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = bq-19q-\frac{10}{3}b+\frac{10}{3}.19& \text{Uitwerken } \\ & =bq-19q-\frac{10}{3}b+\frac{190}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}((-16)-b)(\frac{-13}{10}+b)& =(\color{red}{-b}+\color{orange}{(-16)}).(\color{green}{b}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(-16)} . \color{green}{(b)} + \color{orange}{(-16)} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{13}{10}b-16b+16.\frac{13}{10}& \text{Uitwerken } \\ & =-b^2+(\frac{13}{10}+(-16))b+(\frac{-208}{10}) & \text{Neem samen} \\ &=-b^2-\frac{147}{10}b+(\frac{-208}{10}) & \text{Maak de som} \\ &=-b^2-\frac{147}{10}b+(\frac{-104}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(p+\frac{18}{2})(p+\frac{7}{13})& =(\color{red}{p}+\color{orange}{9}).(\color{green}{p}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(9)} . \color{green}{(p)} + \color{orange}{(9)} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{13}p+9p+9.\frac{7}{13}& \text{Uitwerken } \\ & =p^2+(\frac{7}{13}+9)p+\frac{63}{13} & \text{Neem samen} \\ &=p^2+\frac{124}{13}p+\frac{63}{13} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-15 13:28:40
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