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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{12}{7})(b+\frac{-13}{9})& =(\color{red}{a}+\color{orange}{\frac{12}{7}}).(\color{green}{b}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{12}{7})} . \color{green}{(b)} + \color{orange}{(\frac{12}{7})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{9}a+\frac{12}{7}b-\frac{12}{7}.\frac{13}{9}& \text{Uitwerken } \\ & =ab-\frac{13}{9}a+\frac{12}{7}b-\frac{156}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{13}{9}a+\frac{12}{7}b-\frac{52}{21} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{2}{9}+a)(\frac{12}{14}+x)& =(\color{red}{a}+\color{orange}{\frac{2}{9}}).(\color{green}{x}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{2}{9})} . \color{green}{(x)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{7}a+\frac{2}{9}x+\frac{2}{9}.\frac{6}{7}& \text{Uitwerken } \\ & =ax+\frac{6}{7}a+\frac{2}{9}x+\frac{12}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{6}{7}a+\frac{2}{9}x+\frac{4}{21} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-19}{14})(x+\frac{-12}{2})& =(\color{red}{p}+\color{orange}{\frac{-19}{14}}).(\color{green}{x}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-6)} + \color{orange}{(\frac{-19}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = px-6p-\frac{19}{14}x+\frac{19}{14}.6& \text{Uitwerken } \\ & =px-6p-\frac{19}{14}x+\frac{114}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-6p-\frac{19}{14}x+\frac{57}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{9}{16})(\frac{3}{14}-q)& =(\color{red}{a}+\color{orange}{\frac{-9}{16}}).(\color{green}{-q}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{14}a+\frac{9}{16}q-\frac{9}{16}.\frac{3}{14}& \text{Uitwerken } \\ & =-aq+\frac{3}{14}a+\frac{9}{16}q-\frac{27}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-1}{17}+q)(\frac{9}{11}+q)& =(\color{red}{q}+\color{orange}{\frac{-1}{17}}).(\color{green}{q}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{9}{11}q-\frac{1}{17}q-\frac{1}{17}.\frac{9}{11}& \text{Uitwerken } \\ & =q^2+(\frac{9}{11}+(\frac{-1}{17}))q-(\frac{-9}{187}) & \text{Neem samen} \\ &=q^2+\frac{142}{187}q-(\frac{-9}{187}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{16}{16}+q)(q-\frac{18}{13})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{18}{13}q+1q-1.\frac{18}{13}& \text{Uitwerken } \\ & =q^2+((\frac{-18}{13})+1)q-(\frac{-18}{13}) & \text{Neem samen} \\ &=q^2-\frac{5}{13}q-(\frac{-18}{13}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{2}-p)(a+\frac{-18}{2})& =(\color{red}{-p}+\color{orange}{\frac{13}{2}}).(\color{green}{a}+\color{blue}{(-9)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-9)} + \color{orange}{(\frac{13}{2})} . \color{green}{(a)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -ap+9p+\frac{13}{2}a-\frac{13}{2}.9& \text{Uitwerken } \\ & =-ap+9p+\frac{13}{2}a-\frac{117}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-16}{19}+a)(a-\frac{1}{8})& =(\color{red}{a}+\color{orange}{\frac{-16}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{8}a-\frac{16}{19}a+\frac{16}{19}.\frac{1}{8}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{8})+(\frac{-16}{19}))a+\frac{16}{152} & \text{Neem samen} \\ &=a^2-\frac{147}{152}a+\frac{16}{152} & \text{Maak de som} \\ &=a^2-\frac{147}{152}a+\frac{2}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{20}{7}-x)(\frac{-18}{5}-x)& =(\color{red}{-x}+\color{orange}{\frac{20}{7}}).(\color{green}{-x}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{20}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{18}{5}x-\frac{20}{7}x-\frac{20}{7}.\frac{18}{5}& \text{Uitwerken } \\ & =x^2+(\frac{18}{5}+(\frac{-20}{7}))x-(\frac{-360}{35}) & \text{Neem samen} \\ &=x^2+\frac{26}{35}x-(\frac{-360}{35}) & \text{Maak de som} \\ &=x^2+\frac{26}{35}x+\frac{72}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-17}{14})(\frac{-8}{20}-x)& =(\color{red}{b}+\color{orange}{\frac{17}{14}}).(\color{green}{-x}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{17}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{2}{5}b-\frac{17}{14}x-\frac{17}{14}.\frac{2}{5}& \text{Uitwerken } \\ & =-bx-\frac{2}{5}b-\frac{17}{14}x-\frac{34}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{2}{5}b-\frac{17}{14}x-\frac{17}{35} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{20}{14}+x)(\frac{-17}{4}-x)& =(\color{red}{x}+\color{orange}{\frac{10}{7}}).(\color{green}{-x}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{17}{4}x-\frac{10}{7}x-\frac{10}{7}.\frac{17}{4}& \text{Uitwerken } \\ & =-x^2+((\frac{-17}{4})+(\frac{-10}{7}))x-\frac{170}{28} & \text{Neem samen} \\ &=-x^2-\frac{159}{28}x-\frac{170}{28} & \text{Maak de som} \\ &=-x^2-\frac{159}{28}x-\frac{85}{14} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-9}{15})(x-\frac{7}{14})& =(\color{red}{a}+\color{orange}{\frac{-3}{5}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}a-\frac{3}{5}x+\frac{3}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}a-\frac{3}{5}x+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-18 18:41:43
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