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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{6}{4}-q)(\frac{-10}{18}+p)& =(\color{red}{-q}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{9}q+\frac{3}{2}p-\frac{3}{2}.\frac{5}{9}& \text{Uitwerken } \\ & =-pq+\frac{5}{9}q+\frac{3}{2}p-\frac{15}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{5}{9}q+\frac{3}{2}p-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-11}{17})(\frac{-3}{11}-b)& =(\color{red}{p}+\color{orange}{\frac{-11}{17}}).(\color{green}{-b}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{-11}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{11}p+\frac{11}{17}b+\frac{11}{17}.\frac{3}{11}& \text{Uitwerken } \\ & =-bp-\frac{3}{11}p+\frac{11}{17}b+\frac{33}{187} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{3}{11}p+\frac{11}{17}b+\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-7}{12})(a+\frac{11}{4})& =(\color{red}{a}+\color{orange}{\frac{-7}{12}}).(\color{green}{a}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{11}{4}a-\frac{7}{12}a-\frac{7}{12}.\frac{11}{4}& \text{Uitwerken } \\ & =a^2+(\frac{11}{4}+(\frac{-7}{12}))a-(\frac{-77}{48}) & \text{Neem samen} \\ &=a^2+\frac{26}{12}a-(\frac{-77}{48}) & \text{Maak de som} \\ &=a^2+\frac{13}{6}a+\frac{77}{48} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{16}-b)(6-x)& =(\color{red}{-b}+\color{orange}{\frac{-3}{8}}).(\color{green}{-x}+\color{blue}{6})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(6)} + \color{orange}{(\frac{-3}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bx-6b+\frac{3}{8}x-\frac{3}{8}.6& \text{Uitwerken } \\ & =bx-6b+\frac{3}{8}x-\frac{18}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-6b+\frac{3}{8}x-\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{3}-q)(b+\frac{1}{7})& =(\color{red}{-q}+\color{orange}{\frac{14}{3}}).(\color{green}{b}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{14}{3})} . \color{green}{(b)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{7}q+\frac{14}{3}b+\frac{14}{3}.\frac{1}{7}& \text{Uitwerken } \\ & =-bq-\frac{1}{7}q+\frac{14}{3}b+\frac{14}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{7}q+\frac{14}{3}b+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-9}{2})(\frac{-9}{8}-x)& =(\color{red}{x}+\color{orange}{\frac{-9}{2}}).(\color{green}{-x}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{9}{8}x+\frac{9}{2}x+\frac{9}{2}.\frac{9}{8}& \text{Uitwerken } \\ & =-x^2+((\frac{-9}{8})+\frac{9}{2})x+(\frac{-81}{16}) & \text{Neem samen} \\ &=-x^2+\frac{27}{8}x+(\frac{-81}{16}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{19}-a)(\frac{-17}{14}-q)& =(\color{red}{-a}+\color{orange}{\frac{9}{19}}).(\color{green}{-q}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{9}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{14}a-\frac{9}{19}q-\frac{9}{19}.\frac{17}{14}& \text{Uitwerken } \\ & =aq+\frac{17}{14}a-\frac{9}{19}q-\frac{153}{266} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-15}{18})(\frac{14}{16}+a)& =(\color{red}{q}+\color{orange}{\frac{5}{6}}).(\color{green}{a}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{8}q+\frac{5}{6}a+\frac{5}{6}.\frac{7}{8}& \text{Uitwerken } \\ & =aq+\frac{7}{8}q+\frac{5}{6}a+\frac{35}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{12}{10})(\frac{-10}{14}-q)& =(\color{red}{x}+\color{orange}{\frac{-6}{5}}).(\color{green}{-q}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{7}x+\frac{6}{5}q+\frac{6}{5}.\frac{5}{7}& \text{Uitwerken } \\ & =-qx-\frac{5}{7}x+\frac{6}{5}q+\frac{30}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{5}{7}x+\frac{6}{5}q+\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{20}+q)(\frac{3}{12}+q)& =(\color{red}{q}+\color{orange}{\frac{3}{20}}).(\color{green}{q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{3}{20})} . \color{green}{(q)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{4}q+\frac{3}{20}q+\frac{3}{20}.\frac{1}{4}& \text{Uitwerken } \\ & =q^2+(\frac{1}{4}+\frac{3}{20})q+\frac{3}{80} & \text{Neem samen} \\ &=q^2+\frac{8}{20}q+\frac{3}{80} & \text{Maak de som} \\ &=q^2+\frac{2}{5}q+\frac{3}{80} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{8}{8}+x)(a-\frac{-14}{6})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{3}x+1a+1.\frac{7}{3}& \text{Uitwerken } \\ & =ax+\frac{7}{3}x+1a+\frac{7}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-7}{5}-x)(p+\frac{-2}{6})& =(\color{red}{-x}+\color{orange}{\frac{-7}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{3}x-\frac{7}{5}p+\frac{7}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =-px+\frac{1}{3}x-\frac{7}{5}p+\frac{7}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-16 16:10:44
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