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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{13}-a)(x+(-12))& =(\color{red}{-a}+\color{orange}{\frac{9}{13}}).(\color{green}{x}+\color{blue}{(-12)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(-12)} + \color{orange}{(\frac{9}{13})} . \color{green}{(x)} + \color{orange}{(\frac{9}{13})} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = -ax+12a+\frac{9}{13}x-\frac{9}{13}.12& \text{Uitwerken } \\ & =-ax+12a+\frac{9}{13}x-\frac{108}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-4}{18})(p-\frac{-6}{5})& =(\color{red}{b}+\color{orange}{\frac{2}{9}}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{2}{9})} . \color{green}{(p)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{6}{5}b+\frac{2}{9}p+\frac{2}{9}.\frac{6}{5}& \text{Uitwerken } \\ & =bp+\frac{6}{5}b+\frac{2}{9}p+\frac{12}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{6}{5}b+\frac{2}{9}p+\frac{4}{15} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{9}{8}+p)(q+\frac{16}{19})& =(\color{red}{p}+\color{orange}{\frac{9}{8}}).(\color{green}{q}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{16}{19}p+\frac{9}{8}q+\frac{9}{8}.\frac{16}{19}& \text{Uitwerken } \\ & =pq+\frac{16}{19}p+\frac{9}{8}q+\frac{144}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{16}{19}p+\frac{9}{8}q+\frac{18}{19} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-4}{17}+b)(x-\frac{10}{7})& =(\color{red}{b}+\color{orange}{\frac{-4}{17}}).(\color{green}{x}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-4}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{10}{7}b-\frac{4}{17}x+\frac{4}{17}.\frac{10}{7}& \text{Uitwerken } \\ & =bx-\frac{10}{7}b-\frac{4}{17}x+\frac{40}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}((-11)-b)(b-\frac{-14}{7})& =(\color{red}{-b}+\color{orange}{(-11)}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(2)} + \color{orange}{(-11)} . \color{green}{(b)} + \color{orange}{(-11)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bb-2b-11b-11.2& \text{Uitwerken } \\ & =-b^2+((-2)+(-11))b-22 & \text{Neem samen} \\ &=-b^2-13b-22 & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{12}{7}+a)(x-\frac{13}{6})& =(\color{red}{a}+\color{orange}{\frac{12}{7}}).(\color{green}{x}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{12}{7})} . \color{green}{(x)} + \color{orange}{(\frac{12}{7})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{6}a+\frac{12}{7}x-\frac{12}{7}.\frac{13}{6}& \text{Uitwerken } \\ & =ax-\frac{13}{6}a+\frac{12}{7}x-\frac{156}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{13}{6}a+\frac{12}{7}x-\frac{26}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a-\frac{20}{10})(x-\frac{-15}{16})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{15}{16}a-2x-2.\frac{15}{16}& \text{Uitwerken } \\ & =ax+\frac{15}{16}a-2x-\frac{30}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{15}{16}a-2x-\frac{15}{8} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-15}{12})((-19)+q)& =(\color{red}{x}+\color{orange}{\frac{5}{4}}).(\color{green}{q}+\color{blue}{(-19)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-19)} + \color{orange}{(\frac{5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = qx-19x+\frac{5}{4}q-\frac{5}{4}.19& \text{Uitwerken } \\ & =qx-19x+\frac{5}{4}q-\frac{95}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{14}+b)(a-\frac{18}{20})& =(\color{red}{b}+\color{orange}{\frac{2}{7}}).(\color{green}{a}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{2}{7})} . \color{green}{(a)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{10}b+\frac{2}{7}a-\frac{2}{7}.\frac{9}{10}& \text{Uitwerken } \\ & =ab-\frac{9}{10}b+\frac{2}{7}a-\frac{18}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{9}{10}b+\frac{2}{7}a-\frac{9}{35} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-18}{9}-b)(p+\frac{-18}{19})& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{18}{19}b-2p+2.\frac{18}{19}& \text{Uitwerken } \\ & =-bp+\frac{18}{19}b-2p+\frac{36}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{20}{6})(x+\frac{7}{14})& =(\color{red}{x}+\color{orange}{\frac{-10}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{2}x-\frac{10}{3}x-\frac{10}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =x^2+(\frac{1}{2}+(\frac{-10}{3}))x-(\frac{-10}{6}) & \text{Neem samen} \\ &=x^2-\frac{17}{6}x-(\frac{-10}{6}) & \text{Maak de som} \\ &=x^2-\frac{17}{6}x+\frac{5}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{7}-p)(b+\frac{19}{10})& =(\color{red}{-p}+\color{orange}{\frac{-10}{7}}).(\color{green}{b}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{10}p-\frac{10}{7}b-\frac{10}{7}.\frac{19}{10}& \text{Uitwerken } \\ & =-bp-\frac{19}{10}p-\frac{10}{7}b-\frac{190}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{19}{10}p-\frac{10}{7}b-\frac{19}{7} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-05 23:23:15
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