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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-1}{16})((-14)+b)& =(\color{red}{p}+\color{orange}{\frac{1}{16}}).(\color{green}{b}+\color{blue}{(-14)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-14)} + \color{orange}{(\frac{1}{16})} . \color{green}{(b)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = bp-14p+\frac{1}{16}b-\frac{1}{16}.14& \text{Uitwerken } \\ & =bp-14p+\frac{1}{16}b-\frac{14}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-14p+\frac{1}{16}b-\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x-\frac{6}{8})(b+\frac{17}{7})& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{7}x-\frac{3}{4}b-\frac{3}{4}.\frac{17}{7}& \text{Uitwerken } \\ & =bx+\frac{17}{7}x-\frac{3}{4}b-\frac{51}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{2}{4}-p)(\frac{-17}{14}+a)& =(\color{red}{-p}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{17}{14}p+\frac{1}{2}a-\frac{1}{2}.\frac{17}{14}& \text{Uitwerken } \\ & =-ap+\frac{17}{14}p+\frac{1}{2}a-\frac{17}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{19}{17})(\frac{4}{10}+p)& =(\color{red}{x}+\color{orange}{\frac{19}{17}}).(\color{green}{p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{19}{17})} . \color{green}{(p)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{2}{5}x+\frac{19}{17}p+\frac{19}{17}.\frac{2}{5}& \text{Uitwerken } \\ & =px+\frac{2}{5}x+\frac{19}{17}p+\frac{38}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-4}{14})(q+\frac{12}{3})& =(\color{red}{p}+\color{orange}{\frac{2}{7}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{2}{7})} . \color{green}{(q)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = pq+4p+\frac{2}{7}q+\frac{2}{7}.4& \text{Uitwerken } \\ & =pq+4p+\frac{2}{7}q+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{5}{12}-x)(\frac{-20}{17}+q)& =(\color{red}{-x}+\color{orange}{\frac{5}{12}}).(\color{green}{q}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{5}{12})} . \color{green}{(q)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{20}{17}x+\frac{5}{12}q-\frac{5}{12}.\frac{20}{17}& \text{Uitwerken } \\ & =-qx+\frac{20}{17}x+\frac{5}{12}q-\frac{100}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{20}{17}x+\frac{5}{12}q-\frac{25}{51} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{3}{10}-p)(\frac{13}{5}+b)& =(\color{red}{-p}+\color{orange}{\frac{3}{10}}).(\color{green}{b}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{3}{10})} . \color{green}{(b)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{13}{5}p+\frac{3}{10}b+\frac{3}{10}.\frac{13}{5}& \text{Uitwerken } \\ & =-bp-\frac{13}{5}p+\frac{3}{10}b+\frac{39}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{13}{20})(p+\frac{-20}{18})& =(\color{red}{p}+\color{orange}{\frac{13}{20}}).(\color{green}{p}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{13}{20})} . \color{green}{(p)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{10}{9}p+\frac{13}{20}p-\frac{13}{20}.\frac{10}{9}& \text{Uitwerken } \\ & =p^2+((\frac{-10}{9})+\frac{13}{20})p-(\frac{-130}{180}) & \text{Neem samen} \\ &=p^2-\frac{83}{180}p-(\frac{-130}{180}) & \text{Maak de som} \\ &=p^2-\frac{83}{180}p+\frac{13}{18} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-1}{20})(q+\frac{-5}{10})& =(\color{red}{x}+\color{orange}{\frac{1}{20}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{1}{20})} . \color{green}{(q)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{2}x+\frac{1}{20}q-\frac{1}{20}.\frac{1}{2}& \text{Uitwerken } \\ & =qx-\frac{1}{2}x+\frac{1}{20}q-\frac{1}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-16}{5})(a-\frac{13}{2})& =(\color{red}{a}+\color{orange}{\frac{-16}{5}}).(\color{green}{a}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{13}{2}a-\frac{16}{5}a+\frac{16}{5}.\frac{13}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-13}{2})+(\frac{-16}{5}))a+\frac{208}{10} & \text{Neem samen} \\ &=a^2-\frac{97}{10}a+\frac{208}{10} & \text{Maak de som} \\ &=a^2-\frac{97}{10}a+\frac{104}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{11}+a)(p-\frac{-6}{8})& =(\color{red}{a}+\color{orange}{\frac{-3}{11}}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{4}a-\frac{3}{11}p-\frac{3}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =ap+\frac{3}{4}a-\frac{3}{11}p-\frac{9}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{1}{4}+b)(\frac{15}{7}-p)& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{-p}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{15}{7}b-\frac{1}{4}p+\frac{1}{4}.\frac{15}{7}& \text{Uitwerken } \\ & =-bp+\frac{15}{7}b-\frac{1}{4}p+\frac{15}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-31 16:28:14
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