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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-10}{14})(\frac{-8}{2}-x)& =(\color{red}{b}+\color{orange}{\frac{-5}{7}}).(\color{green}{-x}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(-4)} + \color{orange}{(\frac{-5}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -bx-4b+\frac{5}{7}x+\frac{5}{7}.4& \text{Uitwerken } \\ & =-bx-4b+\frac{5}{7}x+\frac{20}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{3}+q)(q+\frac{-5}{10})& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{2}q+\frac{4}{3}q-\frac{4}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{2})+\frac{4}{3})q-(\frac{-4}{6}) & \text{Neem samen} \\ &=q^2+\frac{5}{6}q-(\frac{-4}{6}) & \text{Maak de som} \\ &=q^2+\frac{5}{6}q+\frac{2}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-7}{20})(\frac{1}{9}-x)& =(\color{red}{q}+\color{orange}{\frac{7}{20}}).(\color{green}{-x}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{7}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{9}q-\frac{7}{20}x+\frac{7}{20}.\frac{1}{9}& \text{Uitwerken } \\ & =-qx+\frac{1}{9}q-\frac{7}{20}x+\frac{7}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{10}{13})(p+\frac{11}{13})& =(\color{red}{b}+\color{orange}{\frac{10}{13}}).(\color{green}{p}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{10}{13})} . \color{green}{(p)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{13}b+\frac{10}{13}p+\frac{10}{13}.\frac{11}{13}& \text{Uitwerken } \\ & =bp+\frac{11}{13}b+\frac{10}{13}p+\frac{110}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-2}{13})(\frac{-13}{10}+a)& =(\color{red}{p}+\color{orange}{\frac{2}{13}}).(\color{green}{a}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{2}{13})} . \color{green}{(a)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{10}p+\frac{2}{13}a-\frac{2}{13}.\frac{13}{10}& \text{Uitwerken } \\ & =ap-\frac{13}{10}p+\frac{2}{13}a-\frac{26}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{13}{10}p+\frac{2}{13}a-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{19}+x)(p-\frac{20}{13})& =(\color{red}{x}+\color{orange}{\frac{-14}{19}}).(\color{green}{p}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{20}{13}x-\frac{14}{19}p+\frac{14}{19}.\frac{20}{13}& \text{Uitwerken } \\ & =px-\frac{20}{13}x-\frac{14}{19}p+\frac{280}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{11}{3})(\frac{16}{6}-x)& =(\color{red}{p}+\color{orange}{\frac{11}{3}}).(\color{green}{-x}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{11}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{8}{3}p-\frac{11}{3}x+\frac{11}{3}.\frac{8}{3}& \text{Uitwerken } \\ & =-px+\frac{8}{3}p-\frac{11}{3}x+\frac{88}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{17}-a)(\frac{16}{18}-p)& =(\color{red}{-a}+\color{orange}{\frac{18}{17}}).(\color{green}{-p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{18}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{9}a-\frac{18}{17}p+\frac{18}{17}.\frac{8}{9}& \text{Uitwerken } \\ & =ap-\frac{8}{9}a-\frac{18}{17}p+\frac{144}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{8}{9}a-\frac{18}{17}p+\frac{16}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-17}{20}+a)(\frac{-14}{15}-x)& =(\color{red}{a}+\color{orange}{\frac{-17}{20}}).(\color{green}{-x}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{14}{15}a+\frac{17}{20}x+\frac{17}{20}.\frac{14}{15}& \text{Uitwerken } \\ & =-ax-\frac{14}{15}a+\frac{17}{20}x+\frac{238}{300} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{14}{15}a+\frac{17}{20}x+\frac{119}{150} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-11}{14}-a)(x-\frac{18}{7})& =(\color{red}{-a}+\color{orange}{\frac{-11}{14}}).(\color{green}{x}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{18}{7}a-\frac{11}{14}x+\frac{11}{14}.\frac{18}{7}& \text{Uitwerken } \\ & =-ax+\frac{18}{7}a-\frac{11}{14}x+\frac{198}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{18}{7}a-\frac{11}{14}x+\frac{99}{49} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-6}{13})(q+\frac{-7}{3})& =(\color{red}{q}+\color{orange}{\frac{-6}{13}}).(\color{green}{q}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{3}q-\frac{6}{13}q+\frac{6}{13}.\frac{7}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{3})+(\frac{-6}{13}))q+\frac{42}{39} & \text{Neem samen} \\ &=q^2-\frac{109}{39}q+\frac{42}{39} & \text{Maak de som} \\ &=q^2-\frac{109}{39}q+\frac{14}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{6}{10}-b)(q+\frac{-15}{12})& =(\color{red}{-b}+\color{orange}{\frac{3}{5}}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{4}b+\frac{3}{5}q-\frac{3}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =-bq+\frac{5}{4}b+\frac{3}{5}q-\frac{15}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{5}{4}b+\frac{3}{5}q-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-26 12:51:53
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