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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{5}+q)(a+\frac{-7}{2})& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{2}q+\frac{3}{5}a-\frac{3}{5}.\frac{7}{2}& \text{Uitwerken } \\ & =aq-\frac{7}{2}q+\frac{3}{5}a-\frac{21}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-2}{12}-a)(b+\frac{-8}{11})& =(\color{red}{-a}+\color{orange}{\frac{-1}{6}}).(\color{green}{b}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{8}{11}a-\frac{1}{6}b+\frac{1}{6}.\frac{8}{11}& \text{Uitwerken } \\ & =-ab+\frac{8}{11}a-\frac{1}{6}b+\frac{8}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{8}{11}a-\frac{1}{6}b+\frac{4}{33} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{5}{11}-a)(p+\frac{18}{4})& =(\color{red}{-a}+\color{orange}{\frac{5}{11}}).(\color{green}{p}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{5}{11})} . \color{green}{(p)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{2}a+\frac{5}{11}p+\frac{5}{11}.\frac{9}{2}& \text{Uitwerken } \\ & =-ap-\frac{9}{2}a+\frac{5}{11}p+\frac{45}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{19}+q)(\frac{2}{19}+a)& =(\color{red}{q}+\color{orange}{\frac{-2}{19}}).(\color{green}{a}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{19}q-\frac{2}{19}a-\frac{2}{19}.\frac{2}{19}& \text{Uitwerken } \\ & =aq+\frac{2}{19}q-\frac{2}{19}a-\frac{4}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-6}{3})(a-\frac{-4}{14})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{7}b-2a-2.\frac{2}{7}& \text{Uitwerken } \\ & =ab+\frac{2}{7}b-2a-\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-3}{10})(x-\frac{-19}{14})& =(\color{red}{x}+\color{orange}{\frac{3}{10}}).(\color{green}{x}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{3}{10})} . \color{green}{(x)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{19}{14}x+\frac{3}{10}x+\frac{3}{10}.\frac{19}{14}& \text{Uitwerken } \\ & =x^2+(\frac{19}{14}+\frac{3}{10})x+\frac{57}{140} & \text{Neem samen} \\ &=x^2+\frac{116}{70}x+\frac{57}{140} & \text{Maak de som} \\ &=x^2+\frac{58}{35}x+\frac{57}{140} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(x+\frac{9}{10})(\frac{-17}{12}+a)& =(\color{red}{x}+\color{orange}{\frac{9}{10}}).(\color{green}{a}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{9}{10})} . \color{green}{(a)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{12}x+\frac{9}{10}a-\frac{9}{10}.\frac{17}{12}& \text{Uitwerken } \\ & =ax-\frac{17}{12}x+\frac{9}{10}a-\frac{153}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{17}{12}x+\frac{9}{10}a-\frac{51}{40} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{3}{14}-q)(q-\frac{10}{15})& =(\color{red}{-q}+\color{orange}{\frac{3}{14}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{3}{14})} . \color{green}{(q)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{2}{3}q+\frac{3}{14}q-\frac{3}{14}.\frac{2}{3}& \text{Uitwerken } \\ & =-q^2+(\frac{2}{3}+\frac{3}{14})q-\frac{6}{42} & \text{Neem samen} \\ &=-q^2+\frac{37}{42}q-\frac{6}{42} & \text{Maak de som} \\ &=-q^2+\frac{37}{42}q-\frac{1}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-13}{13})(\frac{-2}{18}+a)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{9}q+1a-1.\frac{1}{9}& \text{Uitwerken } \\ & =aq-\frac{1}{9}q+1a-\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{2}{10}+b)(b+(-2))& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bb-2b+\frac{1}{5}b-\frac{1}{5}.2& \text{Uitwerken } \\ & =b^2+((-2)+\frac{1}{5})b-(\frac{-2}{5}) & \text{Neem samen} \\ &=b^2-\frac{9}{5}b-(\frac{-2}{5}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{9}-p)(\frac{-18}{15}+p)& =(\color{red}{-p}+\color{orange}{\frac{11}{9}}).(\color{green}{p}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{11}{9})} . \color{green}{(p)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{6}{5}p+\frac{11}{9}p-\frac{11}{9}.\frac{6}{5}& \text{Uitwerken } \\ & =-p^2+(\frac{6}{5}+\frac{11}{9})p-\frac{66}{45} & \text{Neem samen} \\ &=-p^2+\frac{109}{45}p-\frac{66}{45} & \text{Maak de som} \\ &=-p^2+\frac{109}{45}p-\frac{22}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}((-14)-q)(x-\frac{12}{19})& =(\color{red}{-q}+\color{orange}{(-14)}).(\color{green}{x}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(-14)} . \color{green}{(x)} + \color{orange}{(-14)} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{12}{19}q-14x+14.\frac{12}{19}& \text{Uitwerken } \\ & =-qx+\frac{12}{19}q-14x+\frac{168}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-18 11:19:37
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