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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-14}{8})(p+\frac{-10}{13})& =(\color{red}{a}+\color{orange}{\frac{-7}{4}}).(\color{green}{p}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{13}a-\frac{7}{4}p+\frac{7}{4}.\frac{10}{13}& \text{Uitwerken } \\ & =ap-\frac{10}{13}a-\frac{7}{4}p+\frac{70}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{10}{13}a-\frac{7}{4}p+\frac{35}{26} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p+\frac{8}{19})(\frac{9}{11}-p)& =(\color{red}{p}+\color{orange}{\frac{8}{19}}).(\color{green}{-p}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{8}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{9}{11}p-\frac{8}{19}p+\frac{8}{19}.\frac{9}{11}& \text{Uitwerken } \\ & =-p^2+(\frac{9}{11}+(\frac{-8}{19}))p+(\frac{-72}{209}) & \text{Neem samen} \\ &=-p^2+\frac{83}{209}p+(\frac{-72}{209}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-10}{5}-a)(q+\frac{5}{17})& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{17}a-2q-2.\frac{5}{17}& \text{Uitwerken } \\ & =-aq-\frac{5}{17}a-2q-\frac{10}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-18}{13}-a)(a+\frac{12}{7})& =(\color{red}{-a}+\color{orange}{\frac{-18}{13}}).(\color{green}{a}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{-18}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{12}{7}a-\frac{18}{13}a-\frac{18}{13}.\frac{12}{7}& \text{Uitwerken } \\ & =-a^2+((\frac{-12}{7})+(\frac{-18}{13}))a-\frac{216}{91} & \text{Neem samen} \\ &=-a^2-\frac{282}{91}a-\frac{216}{91} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a-\frac{5}{19})(\frac{5}{6}+x)& =(\color{red}{a}+\color{orange}{\frac{-5}{19}}).(\color{green}{x}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{6}a-\frac{5}{19}x-\frac{5}{19}.\frac{5}{6}& \text{Uitwerken } \\ & =ax+\frac{5}{6}a-\frac{5}{19}x-\frac{25}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-1}{3}+q)(q-(-18))& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{18})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(18)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = qq+18q-\frac{1}{3}q-\frac{1}{3}.18& \text{Uitwerken } \\ & =q^2+(18+(\frac{-1}{3}))q-(\frac{-18}{3}) & \text{Neem samen} \\ &=q^2+\frac{53}{3}q-(\frac{-18}{3}) & \text{Maak de som} \\ &=q^2+\frac{53}{3}q+6 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{10}+q)(x+\frac{-18}{17})& =(\color{red}{q}+\color{orange}{\frac{11}{10}}).(\color{green}{x}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{11}{10})} . \color{green}{(x)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{18}{17}q+\frac{11}{10}x-\frac{11}{10}.\frac{18}{17}& \text{Uitwerken } \\ & =qx-\frac{18}{17}q+\frac{11}{10}x-\frac{198}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{18}{17}q+\frac{11}{10}x-\frac{99}{85} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-13}{14}+b)(\frac{3}{9}+b)& =(\color{red}{b}+\color{orange}{\frac{-13}{14}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{3}b-\frac{13}{14}b-\frac{13}{14}.\frac{1}{3}& \text{Uitwerken } \\ & =b^2+(\frac{1}{3}+(\frac{-13}{14}))b-(\frac{-13}{42}) & \text{Neem samen} \\ &=b^2-\frac{25}{42}b-(\frac{-13}{42}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(b+\frac{3}{13})(\frac{12}{2}+b)& =(\color{red}{b}+\color{orange}{\frac{3}{13}}).(\color{green}{b}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(6)} + \color{orange}{(\frac{3}{13})} . \color{green}{(b)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bb+6b+\frac{3}{13}b+\frac{3}{13}.6& \text{Uitwerken } \\ & =b^2+(6+\frac{3}{13})b+\frac{18}{13} & \text{Neem samen} \\ &=b^2+\frac{81}{13}b+\frac{18}{13} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{5}{6}+b)(q+\frac{5}{3})& =(\color{red}{b}+\color{orange}{\frac{5}{6}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{3}b+\frac{5}{6}q+\frac{5}{6}.\frac{5}{3}& \text{Uitwerken } \\ & =bq+\frac{5}{3}b+\frac{5}{6}q+\frac{25}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{2}{2})(a-\frac{-11}{5})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{5}p-1a-1.\frac{11}{5}& \text{Uitwerken } \\ & =ap+\frac{11}{5}p-1a-\frac{11}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{16}{5}+b)(q-\frac{-15}{2})& =(\color{red}{b}+\color{orange}{\frac{16}{5}}).(\color{green}{q}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{16}{5})} . \color{green}{(q)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{2}b+\frac{16}{5}q+\frac{16}{5}.\frac{15}{2}& \text{Uitwerken } \\ & =bq+\frac{15}{2}b+\frac{16}{5}q+\frac{240}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{15}{2}b+\frac{16}{5}q+24 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-08 05:57:53
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