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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{16}+x)(b-\frac{-3}{18})& =(\color{red}{x}+\color{orange}{\frac{9}{16}}).(\color{green}{b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{9}{16})} . \color{green}{(b)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{6}x+\frac{9}{16}b+\frac{9}{16}.\frac{1}{6}& \text{Uitwerken } \\ & =bx+\frac{1}{6}x+\frac{9}{16}b+\frac{9}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{1}{6}x+\frac{9}{16}b+\frac{3}{32} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-4}{16})(\frac{1}{3}+q)& =(\color{red}{b}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{3}b-\frac{1}{4}q-\frac{1}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =bq+\frac{1}{3}b-\frac{1}{4}q-\frac{1}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-8}{3})(b-\frac{-14}{10})& =(\color{red}{q}+\color{orange}{\frac{-8}{3}}).(\color{green}{b}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{5}q-\frac{8}{3}b-\frac{8}{3}.\frac{7}{5}& \text{Uitwerken } \\ & =bq+\frac{7}{5}q-\frac{8}{3}b-\frac{56}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-15}{14})(\frac{7}{9}-b)& =(\color{red}{x}+\color{orange}{\frac{-15}{14}}).(\color{green}{-b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{9}x+\frac{15}{14}b-\frac{15}{14}.\frac{7}{9}& \text{Uitwerken } \\ & =-bx+\frac{7}{9}x+\frac{15}{14}b-\frac{105}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{7}{9}x+\frac{15}{14}b-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{3}{2})(p-(-20))& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{20})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(20)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = pp+20p-\frac{3}{2}p-\frac{3}{2}.20& \text{Uitwerken } \\ & =p^2+(20+(\frac{-3}{2}))p-(\frac{-60}{2}) & \text{Neem samen} \\ &=p^2+\frac{37}{2}p-(\frac{-60}{2}) & \text{Maak de som} \\ &=p^2+\frac{37}{2}p+30 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(a+\frac{14}{4})(\frac{2}{3}-q)& =(\color{red}{a}+\color{orange}{\frac{7}{2}}).(\color{green}{-q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{7}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{2}{3}a-\frac{7}{2}q+\frac{7}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =-aq+\frac{2}{3}a-\frac{7}{2}q+\frac{14}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{2}{3}a-\frac{7}{2}q+\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{7}{6}-a)(b+\frac{6}{14})& =(\color{red}{-a}+\color{orange}{\frac{7}{6}}).(\color{green}{b}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{7}{6})} . \color{green}{(b)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{7}a+\frac{7}{6}b+\frac{7}{6}.\frac{3}{7}& \text{Uitwerken } \\ & =-ab-\frac{3}{7}a+\frac{7}{6}b+\frac{21}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{3}{7}a+\frac{7}{6}b+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a+\frac{17}{7})(\frac{10}{15}+q)& =(\color{red}{a}+\color{orange}{\frac{17}{7}}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{17}{7})} . \color{green}{(q)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{3}a+\frac{17}{7}q+\frac{17}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =aq+\frac{2}{3}a+\frac{17}{7}q+\frac{34}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-1}{17})(\frac{1}{19}-x)& =(\color{red}{x}+\color{orange}{\frac{1}{17}}).(\color{green}{-x}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{1}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{19}x-\frac{1}{17}x+\frac{1}{17}.\frac{1}{19}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{19}+(\frac{-1}{17}))x+(\frac{-1}{323}) & \text{Neem samen} \\ &=-x^2-\frac{2}{323}x+(\frac{-1}{323}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{7}{19}-a)(\frac{11}{2}+x)& =(\color{red}{-a}+\color{orange}{\frac{7}{19}}).(\color{green}{x}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{7}{19})} . \color{green}{(x)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{2}a+\frac{7}{19}x+\frac{7}{19}.\frac{11}{2}& \text{Uitwerken } \\ & =-ax-\frac{11}{2}a+\frac{7}{19}x+\frac{77}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{10}{19})(\frac{8}{13}+b)& =(\color{red}{a}+\color{orange}{\frac{10}{19}}).(\color{green}{b}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{10}{19})} . \color{green}{(b)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{13}a+\frac{10}{19}b+\frac{10}{19}.\frac{8}{13}& \text{Uitwerken } \\ & =ab+\frac{8}{13}a+\frac{10}{19}b+\frac{80}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-2}{19})(\frac{-8}{18}+x)& =(\color{red}{a}+\color{orange}{\frac{2}{19}}).(\color{green}{x}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{2}{19})} . \color{green}{(x)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{9}a+\frac{2}{19}x-\frac{2}{19}.\frac{4}{9}& \text{Uitwerken } \\ & =ax-\frac{4}{9}a+\frac{2}{19}x-\frac{8}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-09 14:03:10
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