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

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

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Verbetersleutel

  1. \(\begin{align}(b+\frac{-11}{13})(\frac{-14}{11}+p)& =(\color{red}{b}+\color{orange}{\frac{-11}{13}}).(\color{green}{p}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{14}{11}b-\frac{11}{13}p+\frac{11}{13}.\frac{14}{11}& \text{Uitwerken } \\ & =bp-\frac{14}{11}b-\frac{11}{13}p+\frac{154}{143} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{14}{11}b-\frac{11}{13}p+\frac{14}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{9}{9}+b)(p+\frac{-13}{7})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{7}b+1p-1.\frac{13}{7}& \text{Uitwerken } \\ & =bp-\frac{13}{7}b+1p-\frac{13}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-18}{12})(a+\frac{20}{17})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{20}{17}a+\frac{3}{2}a+\frac{3}{2}.\frac{20}{17}& \text{Uitwerken } \\ & =a^2+(\frac{20}{17}+\frac{3}{2})a+\frac{60}{34} & \text{Neem samen} \\ &=a^2+\frac{91}{34}a+\frac{60}{34} & \text{Maak de som} \\ &=a^2+\frac{91}{34}a+\frac{30}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-14}{15})(q-\frac{15}{7})& =(\color{red}{a}+\color{orange}{\frac{-14}{15}}).(\color{green}{q}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{7}a-\frac{14}{15}q+\frac{14}{15}.\frac{15}{7}& \text{Uitwerken } \\ & =aq-\frac{15}{7}a-\frac{14}{15}q+\frac{210}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{15}{7}a-\frac{14}{15}q+2 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x-(-2))(q+\frac{8}{12})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{3}x+2q+2.\frac{2}{3}& \text{Uitwerken } \\ & =qx+\frac{2}{3}x+2q+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{11}{18}+b)(b-\frac{-14}{11})& =(\color{red}{b}+\color{orange}{\frac{11}{18}}).(\color{green}{b}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{11}{18})} . \color{green}{(b)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{14}{11}b+\frac{11}{18}b+\frac{11}{18}.\frac{14}{11}& \text{Uitwerken } \\ & =b^2+(\frac{14}{11}+\frac{11}{18})b+\frac{154}{198} & \text{Neem samen} \\ &=b^2+\frac{373}{198}b+\frac{154}{198} & \text{Maak de som} \\ &=b^2+\frac{373}{198}b+\frac{7}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(p+\frac{10}{7})(\frac{-2}{19}-p)& =(\color{red}{p}+\color{orange}{\frac{10}{7}}).(\color{green}{-p}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{2}{19}p-\frac{10}{7}p-\frac{10}{7}.\frac{2}{19}& \text{Uitwerken } \\ & =-p^2+((\frac{-2}{19})+(\frac{-10}{7}))p-\frac{20}{133} & \text{Neem samen} \\ &=-p^2-\frac{204}{133}p-\frac{20}{133} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{6}+x)(\frac{9}{19}+a)& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{19}x+\frac{2}{3}a+\frac{2}{3}.\frac{9}{19}& \text{Uitwerken } \\ & =ax+\frac{9}{19}x+\frac{2}{3}a+\frac{18}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{9}{19}x+\frac{2}{3}a+\frac{6}{19} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{7}{10}+p)(p-\frac{15}{5})& =(\color{red}{p}+\color{orange}{\frac{7}{10}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pp-3p+\frac{7}{10}p-\frac{7}{10}.3& \text{Uitwerken } \\ & =p^2+((-3)+\frac{7}{10})p-(\frac{-21}{10}) & \text{Neem samen} \\ &=p^2-\frac{23}{10}p-(\frac{-21}{10}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-13}{20}+b)(\frac{20}{14}-a)& =(\color{red}{b}+\color{orange}{\frac{-13}{20}}).(\color{green}{-a}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{10}{7}b+\frac{13}{20}a-\frac{13}{20}.\frac{10}{7}& \text{Uitwerken } \\ & =-ab+\frac{10}{7}b+\frac{13}{20}a-\frac{130}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{10}{7}b+\frac{13}{20}a-\frac{13}{14} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-4}{5}-q)(\frac{6}{11}+p)& =(\color{red}{-q}+\color{orange}{\frac{-4}{5}}).(\color{green}{p}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{6}{11}q-\frac{4}{5}p-\frac{4}{5}.\frac{6}{11}& \text{Uitwerken } \\ & =-pq-\frac{6}{11}q-\frac{4}{5}p-\frac{24}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{16}+p)(\frac{4}{16}+x)& =(\color{red}{p}+\color{orange}{\frac{-9}{8}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{4}p-\frac{9}{8}x-\frac{9}{8}.\frac{1}{4}& \text{Uitwerken } \\ & =px+\frac{1}{4}p-\frac{9}{8}x-\frac{9}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-06 00:09:07
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