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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-3}{5})(\frac{4}{18}+b)& =(\color{red}{p}+\color{orange}{\frac{3}{5}}).(\color{green}{b}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{9}p+\frac{3}{5}b+\frac{3}{5}.\frac{2}{9}& \text{Uitwerken } \\ & =bp+\frac{2}{9}p+\frac{3}{5}b+\frac{6}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{9}p+\frac{3}{5}b+\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{17}{16}-p)(\frac{3}{13}-a)& =(\color{red}{-p}+\color{orange}{\frac{17}{16}}).(\color{green}{-a}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{17}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{13}p-\frac{17}{16}a+\frac{17}{16}.\frac{3}{13}& \text{Uitwerken } \\ & =ap-\frac{3}{13}p-\frac{17}{16}a+\frac{51}{208} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{10}{6})(p+\frac{-17}{12})& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{p}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{12}p-\frac{5}{3}p+\frac{5}{3}.\frac{17}{12}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{12})+(\frac{-5}{3}))p+\frac{85}{36} & \text{Neem samen} \\ &=p^2-\frac{37}{12}p+\frac{85}{36} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-12}{6})(\frac{5}{4}-b)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{-b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(2)} . \color{green}{(-b)} + \color{orange}{(2)} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{4}a-2b+2.\frac{5}{4}& \text{Uitwerken } \\ & =-ab+\frac{5}{4}a-2b+\frac{10}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{4}a-2b+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{7}{14}+p)(\frac{18}{16}+p)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{8}p+\frac{1}{2}p+\frac{1}{2}.\frac{9}{8}& \text{Uitwerken } \\ & =p^2+(\frac{9}{8}+\frac{1}{2})p+\frac{9}{16} & \text{Neem samen} \\ &=p^2+\frac{13}{8}p+\frac{9}{16} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-5}{14}-x)(a+\frac{-14}{3})& =(\color{red}{-x}+\color{orange}{\frac{-5}{14}}).(\color{green}{a}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{14}{3}x-\frac{5}{14}a+\frac{5}{14}.\frac{14}{3}& \text{Uitwerken } \\ & =-ax+\frac{14}{3}x-\frac{5}{14}a+\frac{70}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{14}{3}x-\frac{5}{14}a+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a+\frac{2}{15})(q+\frac{13}{4})& =(\color{red}{a}+\color{orange}{\frac{2}{15}}).(\color{green}{q}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{2}{15})} . \color{green}{(q)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{4}a+\frac{2}{15}q+\frac{2}{15}.\frac{13}{4}& \text{Uitwerken } \\ & =aq+\frac{13}{4}a+\frac{2}{15}q+\frac{26}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{13}{4}a+\frac{2}{15}q+\frac{13}{30} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-11}{20})(\frac{-7}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{-11}{20}}).(\color{green}{p}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{4}a-\frac{11}{20}p+\frac{11}{20}.\frac{7}{4}& \text{Uitwerken } \\ & =ap-\frac{7}{4}a-\frac{11}{20}p+\frac{77}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-20}{12})(x-\frac{16}{5})& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{x}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{16}{5}x+\frac{5}{3}x-\frac{5}{3}.\frac{16}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-16}{5})+\frac{5}{3})x-(\frac{-80}{15}) & \text{Neem samen} \\ &=x^2-\frac{23}{15}x-(\frac{-80}{15}) & \text{Maak de som} \\ &=x^2-\frac{23}{15}x+\frac{16}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(b-\frac{8}{3})(\frac{-10}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{-8}{3}}).(\color{green}{p}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{9}b-\frac{8}{3}p+\frac{8}{3}.\frac{5}{9}& \text{Uitwerken } \\ & =bp-\frac{5}{9}b-\frac{8}{3}p+\frac{40}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{2}{7}-q)(\frac{12}{5}+b)& =(\color{red}{-q}+\color{orange}{\frac{2}{7}}).(\color{green}{b}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{2}{7})} . \color{green}{(b)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{12}{5}q+\frac{2}{7}b+\frac{2}{7}.\frac{12}{5}& \text{Uitwerken } \\ & =-bq-\frac{12}{5}q+\frac{2}{7}b+\frac{24}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-13}{17})(\frac{-11}{2}+x)& =(\color{red}{q}+\color{orange}{\frac{13}{17}}).(\color{green}{x}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{13}{17})} . \color{green}{(x)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{2}q+\frac{13}{17}x-\frac{13}{17}.\frac{11}{2}& \text{Uitwerken } \\ & =qx-\frac{11}{2}q+\frac{13}{17}x-\frac{143}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-16 11:35:40
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