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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{20}-x)(x+\frac{5}{3})& =(\color{red}{-x}+\color{orange}{\frac{11}{20}}).(\color{green}{x}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{11}{20})} . \color{green}{(x)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{5}{3}x+\frac{11}{20}x+\frac{11}{20}.\frac{5}{3}& \text{Uitwerken } \\ & =-x^2+((\frac{-5}{3})+\frac{11}{20})x+(\frac{-55}{60}) & \text{Neem samen} \\ &=-x^2-\frac{67}{60}x+(\frac{-55}{60}) & \text{Maak de som} \\ &=-x^2-\frac{67}{60}x+(\frac{-11}{12}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{17}{12}-b)(\frac{17}{2}-x)& =(\color{red}{-b}+\color{orange}{\frac{17}{12}}).(\color{green}{-x}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(\frac{17}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{2}b-\frac{17}{12}x+\frac{17}{12}.\frac{17}{2}& \text{Uitwerken } \\ & =bx-\frac{17}{2}b-\frac{17}{12}x+\frac{289}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{9}-a)(x+\frac{14}{18})& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{9}a-2x-2.\frac{7}{9}& \text{Uitwerken } \\ & =-ax-\frac{7}{9}a-2x-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-11}{13}-x)(p-\frac{9}{5})& =(\color{red}{-x}+\color{orange}{\frac{-11}{13}}).(\color{green}{p}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{9}{5}x-\frac{11}{13}p+\frac{11}{13}.\frac{9}{5}& \text{Uitwerken } \\ & =-px+\frac{9}{5}x-\frac{11}{13}p+\frac{99}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-5}{17}+a)(\frac{-3}{10}-p)& =(\color{red}{a}+\color{orange}{\frac{-5}{17}}).(\color{green}{-p}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{10}a+\frac{5}{17}p+\frac{5}{17}.\frac{3}{10}& \text{Uitwerken } \\ & =-ap-\frac{3}{10}a+\frac{5}{17}p+\frac{15}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{3}{10}a+\frac{5}{17}p+\frac{3}{34} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-10}{15}+q)(\frac{3}{2}-a)& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{-a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{2}q+\frac{2}{3}a-\frac{2}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =-aq+\frac{3}{2}q+\frac{2}{3}a-\frac{6}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{3}{2}q+\frac{2}{3}a-1 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a+\frac{1}{19})(x+\frac{-14}{5})& =(\color{red}{a}+\color{orange}{\frac{1}{19}}).(\color{green}{x}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{1}{19})} . \color{green}{(x)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{14}{5}a+\frac{1}{19}x-\frac{1}{19}.\frac{14}{5}& \text{Uitwerken } \\ & =ax-\frac{14}{5}a+\frac{1}{19}x-\frac{14}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{12}+q)(x+\frac{2}{17})& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{17}q+\frac{3}{2}x+\frac{3}{2}.\frac{2}{17}& \text{Uitwerken } \\ & =qx+\frac{2}{17}q+\frac{3}{2}x+\frac{6}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{2}{17}q+\frac{3}{2}x+\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{14}{3})(a-\frac{7}{9})& =(\color{red}{b}+\color{orange}{\frac{14}{3}}).(\color{green}{a}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{14}{3})} . \color{green}{(a)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{9}b+\frac{14}{3}a-\frac{14}{3}.\frac{7}{9}& \text{Uitwerken } \\ & =ab-\frac{7}{9}b+\frac{14}{3}a-\frac{98}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{13}{12}-a)(q-\frac{11}{6})& =(\color{red}{-a}+\color{orange}{\frac{13}{12}}).(\color{green}{q}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{13}{12})} . \color{green}{(q)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{11}{6}a+\frac{13}{12}q-\frac{13}{12}.\frac{11}{6}& \text{Uitwerken } \\ & =-aq+\frac{11}{6}a+\frac{13}{12}q-\frac{143}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-9}{16})(a-\frac{9}{15})& =(\color{red}{p}+\color{orange}{\frac{-9}{16}}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{5}p-\frac{9}{16}a+\frac{9}{16}.\frac{3}{5}& \text{Uitwerken } \\ & =ap-\frac{3}{5}p-\frac{9}{16}a+\frac{27}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{9}{19})(\frac{-18}{19}+p)& =(\color{red}{b}+\color{orange}{\frac{-9}{19}}).(\color{green}{p}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{18}{19}b-\frac{9}{19}p+\frac{9}{19}.\frac{18}{19}& \text{Uitwerken } \\ & =bp-\frac{18}{19}b-\frac{9}{19}p+\frac{162}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-13 01:49:50
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