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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-2}{17}+a)(\frac{-7}{18}-x)& =(\color{red}{a}+\color{orange}{\frac{-2}{17}}).(\color{green}{-x}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{18}a+\frac{2}{17}x+\frac{2}{17}.\frac{7}{18}& \text{Uitwerken } \\ & =-ax-\frac{7}{18}a+\frac{2}{17}x+\frac{14}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{7}{18}a+\frac{2}{17}x+\frac{7}{153} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{11}-a)(\frac{13}{2}-p)& =(\color{red}{-a}+\color{orange}{\frac{4}{11}}).(\color{green}{-p}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{4}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{2}a-\frac{4}{11}p+\frac{4}{11}.\frac{13}{2}& \text{Uitwerken } \\ & =ap-\frac{13}{2}a-\frac{4}{11}p+\frac{52}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{13}{2}a-\frac{4}{11}p+\frac{26}{11} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{3}-a)(a-\frac{7}{12})& =(\color{red}{-a}+\color{orange}{\frac{-14}{3}}).(\color{green}{a}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{7}{12}a-\frac{14}{3}a+\frac{14}{3}.\frac{7}{12}& \text{Uitwerken } \\ & =-a^2+(\frac{7}{12}+(\frac{-14}{3}))a+(\frac{-98}{36}) & \text{Neem samen} \\ &=-a^2-\frac{49}{12}a+(\frac{-98}{36}) & \text{Maak de som} \\ &=-a^2-\frac{49}{12}a+(\frac{-49}{18}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(a-\frac{3}{7})(\frac{-16}{19}+a)& =(\color{red}{a}+\color{orange}{\frac{-3}{7}}).(\color{green}{a}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{16}{19}a-\frac{3}{7}a+\frac{3}{7}.\frac{16}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-16}{19})+(\frac{-3}{7}))a+\frac{48}{133} & \text{Neem samen} \\ &=a^2-\frac{169}{133}a+\frac{48}{133} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-12}{4})(\frac{3}{13}-x)& =(\color{red}{q}+\color{orange}{3}).(\color{green}{-x}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(3)} . \color{green}{(-x)} + \color{orange}{(3)} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{13}q-3x+3.\frac{3}{13}& \text{Uitwerken } \\ & =-qx+\frac{3}{13}q-3x+\frac{9}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{16}{3})(\frac{18}{2}+b)& =(\color{red}{x}+\color{orange}{\frac{16}{3}}).(\color{green}{b}+\color{blue}{9})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(9)} + \color{orange}{(\frac{16}{3})} . \color{green}{(b)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = bx+9x+\frac{16}{3}b+\frac{16}{3}.9& \text{Uitwerken } \\ & =bx+9x+\frac{16}{3}b+\frac{144}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+9x+\frac{16}{3}b+48 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q+\frac{4}{9})(\frac{11}{14}-p)& =(\color{red}{q}+\color{orange}{\frac{4}{9}}).(\color{green}{-p}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(\frac{4}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{14}q-\frac{4}{9}p+\frac{4}{9}.\frac{11}{14}& \text{Uitwerken } \\ & =-pq+\frac{11}{14}q-\frac{4}{9}p+\frac{44}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{11}{14}q-\frac{4}{9}p+\frac{22}{63} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-20}{20})(a+\frac{15}{13})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{15}{13}p+1a+1.\frac{15}{13}& \text{Uitwerken } \\ & =ap+\frac{15}{13}p+1a+\frac{15}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{7}{15})(q-\frac{-17}{5})& =(\color{red}{b}+\color{orange}{\frac{-7}{15}}).(\color{green}{q}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{5}b-\frac{7}{15}q-\frac{7}{15}.\frac{17}{5}& \text{Uitwerken } \\ & =bq+\frac{17}{5}b-\frac{7}{15}q-\frac{119}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-17}{10})(\frac{12}{6}-a)& =(\color{red}{p}+\color{orange}{\frac{-17}{10}}).(\color{green}{-a}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ap+2p+\frac{17}{10}a-\frac{17}{10}.2& \text{Uitwerken } \\ & =-ap+2p+\frac{17}{10}a-\frac{34}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+2p+\frac{17}{10}a-\frac{17}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-2}{16}+p)(a-\frac{9}{6})& =(\color{red}{p}+\color{orange}{\frac{-1}{8}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{2}p-\frac{1}{8}a+\frac{1}{8}.\frac{3}{2}& \text{Uitwerken } \\ & =ap-\frac{3}{2}p-\frac{1}{8}a+\frac{3}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-8}{14}-x)(\frac{6}{11}+p)& =(\color{red}{-x}+\color{orange}{\frac{-4}{7}}).(\color{green}{p}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{6}{11}x-\frac{4}{7}p-\frac{4}{7}.\frac{6}{11}& \text{Uitwerken } \\ & =-px-\frac{6}{11}x-\frac{4}{7}p-\frac{24}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-21 18:15:05
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