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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{13}-b)(q-\frac{2}{8})& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{4}b-1q+1.\frac{1}{4}& \text{Uitwerken } \\ & =-bq+\frac{1}{4}b-1q+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-13}{7}-x)(a+\frac{1}{5})& =(\color{red}{-x}+\color{orange}{\frac{-13}{7}}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{5}x-\frac{13}{7}a-\frac{13}{7}.\frac{1}{5}& \text{Uitwerken } \\ & =-ax-\frac{1}{5}x-\frac{13}{7}a-\frac{13}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{4}{4}+x)(\frac{14}{7}+a)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2x+1a+1.2& \text{Uitwerken } \\ & =ax+2x+1a+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-5}{9})(\frac{-4}{3}-b)& =(\color{red}{q}+\color{orange}{\frac{-5}{9}}).(\color{green}{-b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{4}{3}q+\frac{5}{9}b+\frac{5}{9}.\frac{4}{3}& \text{Uitwerken } \\ & =-bq-\frac{4}{3}q+\frac{5}{9}b+\frac{20}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{16}+x)(q-\frac{-3}{13})& =(\color{red}{x}+\color{orange}{\frac{-15}{16}}).(\color{green}{q}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{13}x-\frac{15}{16}q-\frac{15}{16}.\frac{3}{13}& \text{Uitwerken } \\ & =qx+\frac{3}{13}x-\frac{15}{16}q-\frac{45}{208} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+19)(x+\frac{10}{2})& =(\color{red}{q}+\color{orange}{19}).(\color{green}{x}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(19)} . \color{green}{(x)} + \color{orange}{(19)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = qx+5q+19x+19.5& \text{Uitwerken } \\ & =qx+5q+19x+95 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{11}{17})(x+\frac{-18}{16})& =(\color{red}{q}+\color{orange}{\frac{11}{17}}).(\color{green}{x}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{11}{17})} . \color{green}{(x)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{8}q+\frac{11}{17}x-\frac{11}{17}.\frac{9}{8}& \text{Uitwerken } \\ & =qx-\frac{9}{8}q+\frac{11}{17}x-\frac{99}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{14}{5}+x)(\frac{18}{2}+p)& =(\color{red}{x}+\color{orange}{\frac{14}{5}}).(\color{green}{p}+\color{blue}{9})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(9)} + \color{orange}{(\frac{14}{5})} . \color{green}{(p)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = px+9x+\frac{14}{5}p+\frac{14}{5}.9& \text{Uitwerken } \\ & =px+9x+\frac{14}{5}p+\frac{126}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{13}{10})(x+\frac{18}{8})& =(\color{red}{a}+\color{orange}{\frac{-13}{10}}).(\color{green}{x}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{4}a-\frac{13}{10}x-\frac{13}{10}.\frac{9}{4}& \text{Uitwerken } \\ & =ax+\frac{9}{4}a-\frac{13}{10}x-\frac{117}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{-10}{12})(a+\frac{-19}{5})& =(\color{red}{x}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{5}x-\frac{5}{6}a+\frac{5}{6}.\frac{19}{5}& \text{Uitwerken } \\ & =ax-\frac{19}{5}x-\frac{5}{6}a+\frac{95}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{19}{5}x-\frac{5}{6}a+\frac{19}{6} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-2}{19}+a)(a+\frac{-13}{8})& =(\color{red}{a}+\color{orange}{\frac{-2}{19}}).(\color{green}{a}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{13}{8}a-\frac{2}{19}a+\frac{2}{19}.\frac{13}{8}& \text{Uitwerken } \\ & =a^2+((\frac{-13}{8})+(\frac{-2}{19}))a+\frac{26}{152} & \text{Neem samen} \\ &=a^2-\frac{263}{152}a+\frac{26}{152} & \text{Maak de som} \\ &=a^2-\frac{263}{152}a+\frac{13}{76} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{8}-b)(q+\frac{-17}{15})& =(\color{red}{-b}+\color{orange}{\frac{-9}{8}}).(\color{green}{q}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{17}{15}b-\frac{9}{8}q+\frac{9}{8}.\frac{17}{15}& \text{Uitwerken } \\ & =-bq+\frac{17}{15}b-\frac{9}{8}q+\frac{153}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{17}{15}b-\frac{9}{8}q+\frac{51}{40} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-03 01:06:47
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