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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{-8}{15})(q+\frac{-2}{5})& =(\color{red}{x}+\color{orange}{\frac{-8}{15}}).(\color{green}{q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{5}x-\frac{8}{15}q+\frac{8}{15}.\frac{2}{5}& \text{Uitwerken } \\ & =qx-\frac{2}{5}x-\frac{8}{15}q+\frac{16}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{10}+a)(q+\frac{16}{6})& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{q}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{3}a+\frac{6}{5}q+\frac{6}{5}.\frac{8}{3}& \text{Uitwerken } \\ & =aq+\frac{8}{3}a+\frac{6}{5}q+\frac{48}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{8}{3}a+\frac{6}{5}q+\frac{16}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-9}{18}-a)(p-\frac{-19}{4})& =(\color{red}{-a}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{19}{4}a-\frac{1}{2}p-\frac{1}{2}.\frac{19}{4}& \text{Uitwerken } \\ & =-ap-\frac{19}{4}a-\frac{1}{2}p-\frac{19}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-12}{2}+b)(q+\frac{20}{7})& =(\color{red}{b}+\color{orange}{(-6)}).(\color{green}{q}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(-6)} . \color{green}{(q)} + \color{orange}{(-6)} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{20}{7}b-6q-6.\frac{20}{7}& \text{Uitwerken } \\ & =bq+\frac{20}{7}b-6q-\frac{120}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{6}{18}-x)(\frac{-14}{17}-b)& =(\color{red}{-x}+\color{orange}{\frac{1}{3}}).(\color{green}{-b}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{14}{17}x-\frac{1}{3}b-\frac{1}{3}.\frac{14}{17}& \text{Uitwerken } \\ & =bx+\frac{14}{17}x-\frac{1}{3}b-\frac{14}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-8}{20}+x)(x-\frac{7}{13})& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{x}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{7}{13}x-\frac{2}{5}x+\frac{2}{5}.\frac{7}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-7}{13})+(\frac{-2}{5}))x+\frac{14}{65} & \text{Neem samen} \\ &=x^2-\frac{61}{65}x+\frac{14}{65} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-11}{16}+b)(p-\frac{-9}{6})& =(\color{red}{b}+\color{orange}{\frac{-11}{16}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{2}b-\frac{11}{16}p-\frac{11}{16}.\frac{3}{2}& \text{Uitwerken } \\ & =bp+\frac{3}{2}b-\frac{11}{16}p-\frac{33}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{13}{16})(\frac{15}{4}+a)& =(\color{red}{p}+\color{orange}{\frac{13}{16}}).(\color{green}{a}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{13}{16})} . \color{green}{(a)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{15}{4}p+\frac{13}{16}a+\frac{13}{16}.\frac{15}{4}& \text{Uitwerken } \\ & =ap+\frac{15}{4}p+\frac{13}{16}a+\frac{195}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-8}{4}-a)(a-\frac{1}{20})& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{20}a-2a+2.\frac{1}{20}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{20}+(-2))a+(\frac{-2}{20}) & \text{Neem samen} \\ &=-a^2-\frac{39}{20}a+(\frac{-2}{20}) & \text{Maak de som} \\ &=-a^2-\frac{39}{20}a+(\frac{-1}{10}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-17}{13})(\frac{-13}{13}-x)& =(\color{red}{a}+\color{orange}{\frac{-17}{13}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-17}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ax-1a+\frac{17}{13}x+\frac{17}{13}.1& \text{Uitwerken } \\ & =-ax-1a+\frac{17}{13}x+\frac{17}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{1}{9})(q+\frac{10}{9})& =(\color{red}{b}+\color{orange}{\frac{-1}{9}}).(\color{green}{q}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{10}{9}b-\frac{1}{9}q-\frac{1}{9}.\frac{10}{9}& \text{Uitwerken } \\ & =bq+\frac{10}{9}b-\frac{1}{9}q-\frac{10}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{6}+b)(\frac{-3}{13}+a)& =(\color{red}{b}+\color{orange}{\frac{13}{6}}).(\color{green}{a}+\color{blue}{\frac{-3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{13})} + \color{orange}{(\frac{13}{6})} . \color{green}{(a)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(\frac{-3}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{13}b+\frac{13}{6}a-\frac{13}{6}.\frac{3}{13}& \text{Uitwerken } \\ & =ab-\frac{3}{13}b+\frac{13}{6}a-\frac{39}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{3}{13}b+\frac{13}{6}a-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-14 17:29:33
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