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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-10}{16}-b)(\frac{-9}{10}-b)& =(\color{red}{-b}+\color{orange}{\frac{-5}{8}}).(\color{green}{-b}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{9}{10}b+\frac{5}{8}b+\frac{5}{8}.\frac{9}{10}& \text{Uitwerken } \\ & =b^2+(\frac{9}{10}+\frac{5}{8})b+\frac{45}{80} & \text{Neem samen} \\ &=b^2+\frac{61}{40}b+\frac{45}{80} & \text{Maak de som} \\ &=b^2+\frac{61}{40}b+\frac{9}{16} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-8}{19}-q)(\frac{-1}{15}-a)& =(\color{red}{-q}+\color{orange}{\frac{-8}{19}}).(\color{green}{-a}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{15}q+\frac{8}{19}a+\frac{8}{19}.\frac{1}{15}& \text{Uitwerken } \\ & =aq+\frac{1}{15}q+\frac{8}{19}a+\frac{8}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{9}-p)((-9)+b)& =(\color{red}{-p}+\color{orange}{\frac{-11}{9}}).(\color{green}{b}+\color{blue}{(-9)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(-9)} + \color{orange}{(\frac{-11}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -bp+9p-\frac{11}{9}b+\frac{11}{9}.9& \text{Uitwerken } \\ & =-bp+9p-\frac{11}{9}b+\frac{99}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+9p-\frac{11}{9}b+11 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{14}{10}+q)(\frac{-1}{4}+q)& =(\color{red}{q}+\color{orange}{\frac{7}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{4}q+\frac{7}{5}q-\frac{7}{5}.\frac{1}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{4})+\frac{7}{5})q-(\frac{-7}{20}) & \text{Neem samen} \\ &=q^2+\frac{23}{20}q-(\frac{-7}{20}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(x+\frac{2}{6})(q+\frac{7}{12})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{12}x+\frac{1}{3}q+\frac{1}{3}.\frac{7}{12}& \text{Uitwerken } \\ & =qx+\frac{7}{12}x+\frac{1}{3}q+\frac{7}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{17}{2}+p)(q-\frac{-20}{15})& =(\color{red}{p}+\color{orange}{\frac{17}{2}}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{17}{2})} . \color{green}{(q)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{3}p+\frac{17}{2}q+\frac{17}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =pq+\frac{4}{3}p+\frac{17}{2}q+\frac{68}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{4}{3}p+\frac{17}{2}q+\frac{34}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(14-x)(p-\frac{17}{6})& =(\color{red}{-x}+\color{orange}{14}).(\color{green}{p}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(14)} . \color{green}{(p)} + \color{orange}{(14)} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{17}{6}x+14p-14.\frac{17}{6}& \text{Uitwerken } \\ & =-px+\frac{17}{6}x+14p-\frac{238}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{17}{6}x+14p-\frac{119}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+(-13))(\frac{16}{10}-q)& =(\color{red}{b}+\color{orange}{(-13)}).(\color{green}{-q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(-13)} . \color{green}{(-q)} + \color{orange}{(-13)} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{8}{5}b+13q-13.\frac{8}{5}& \text{Uitwerken } \\ & =-bq+\frac{8}{5}b+13q-\frac{104}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-10}{12}+a)(p-\frac{16}{13})& =(\color{red}{a}+\color{orange}{\frac{-5}{6}}).(\color{green}{p}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{16}{13}a-\frac{5}{6}p+\frac{5}{6}.\frac{16}{13}& \text{Uitwerken } \\ & =ap-\frac{16}{13}a-\frac{5}{6}p+\frac{80}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{16}{13}a-\frac{5}{6}p+\frac{40}{39} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{20}{7}+x)(\frac{-1}{9}+q)& =(\color{red}{x}+\color{orange}{\frac{20}{7}}).(\color{green}{q}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{20}{7})} . \color{green}{(q)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{9}x+\frac{20}{7}q-\frac{20}{7}.\frac{1}{9}& \text{Uitwerken } \\ & =qx-\frac{1}{9}x+\frac{20}{7}q-\frac{20}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{13}+q)(x-(-8))& =(\color{red}{q}+\color{orange}{\frac{14}{13}}).(\color{green}{x}+\color{blue}{8})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(8)} + \color{orange}{(\frac{14}{13})} . \color{green}{(x)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = qx+8q+\frac{14}{13}x+\frac{14}{13}.8& \text{Uitwerken } \\ & =qx+8q+\frac{14}{13}x+\frac{112}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-18}{4})(p+\frac{13}{5})& =(\color{red}{a}+\color{orange}{\frac{-9}{2}}).(\color{green}{p}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{5}a-\frac{9}{2}p-\frac{9}{2}.\frac{13}{5}& \text{Uitwerken } \\ & =ap+\frac{13}{5}a-\frac{9}{2}p-\frac{117}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-09 05:57:30
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