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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{3}+a)(\frac{9}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{4}a+\frac{4}{3}p+\frac{4}{3}.\frac{9}{4}& \text{Uitwerken } \\ & =ap+\frac{9}{4}a+\frac{4}{3}p+\frac{36}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{9}{4}a+\frac{4}{3}p+3 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{2}{16}+q)(a+\frac{20}{17})& =(\color{red}{q}+\color{orange}{\frac{1}{8}}).(\color{green}{a}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{20}{17}q+\frac{1}{8}a+\frac{1}{8}.\frac{20}{17}& \text{Uitwerken } \\ & =aq+\frac{20}{17}q+\frac{1}{8}a+\frac{20}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{20}{17}q+\frac{1}{8}a+\frac{5}{34} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-4}{20}-b)(x+\frac{18}{18})& =(\color{red}{-b}+\color{orange}{\frac{-1}{5}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx-1b-\frac{1}{5}x-\frac{1}{5}.1& \text{Uitwerken } \\ & =-bx-1b-\frac{1}{5}x-\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{16}-p)(a-\frac{18}{5})& =(\color{red}{-p}+\color{orange}{\frac{-1}{8}}).(\color{green}{a}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{18}{5}p-\frac{1}{8}a+\frac{1}{8}.\frac{18}{5}& \text{Uitwerken } \\ & =-ap+\frac{18}{5}p-\frac{1}{8}a+\frac{18}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{18}{5}p-\frac{1}{8}a+\frac{9}{20} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{2}+q)(b+\frac{3}{17})& =(\color{red}{q}+\color{orange}{(-8)}).(\color{green}{b}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(-8)} . \color{green}{(b)} + \color{orange}{(-8)} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{17}q-8b-8.\frac{3}{17}& \text{Uitwerken } \\ & =bq+\frac{3}{17}q-8b-\frac{24}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{2}{4}+q)(q-\frac{3}{8})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{8}q+\frac{1}{2}q-\frac{1}{2}.\frac{3}{8}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{8})+\frac{1}{2})q-(\frac{-3}{16}) & \text{Neem samen} \\ &=q^2+\frac{1}{8}q-(\frac{-3}{16}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b+\frac{3}{20})(p+\frac{7}{6})& =(\color{red}{b}+\color{orange}{\frac{3}{20}}).(\color{green}{p}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{3}{20})} . \color{green}{(p)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{6}b+\frac{3}{20}p+\frac{3}{20}.\frac{7}{6}& \text{Uitwerken } \\ & =bp+\frac{7}{6}b+\frac{3}{20}p+\frac{21}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{7}{6}b+\frac{3}{20}p+\frac{7}{40} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a+\frac{12}{17})(x+\frac{20}{6})& =(\color{red}{a}+\color{orange}{\frac{12}{17}}).(\color{green}{x}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{12}{17})} . \color{green}{(x)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{10}{3}a+\frac{12}{17}x+\frac{12}{17}.\frac{10}{3}& \text{Uitwerken } \\ & =ax+\frac{10}{3}a+\frac{12}{17}x+\frac{120}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{10}{3}a+\frac{12}{17}x+\frac{40}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-16}{13})(x-\frac{9}{10})& =(\color{red}{q}+\color{orange}{\frac{-16}{13}}).(\color{green}{x}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{10}q-\frac{16}{13}x+\frac{16}{13}.\frac{9}{10}& \text{Uitwerken } \\ & =qx-\frac{9}{10}q-\frac{16}{13}x+\frac{144}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{9}{10}q-\frac{16}{13}x+\frac{72}{65} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-16}{15})(\frac{-17}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{-16}{15}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-16}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a-\frac{16}{15}q+\frac{16}{15}.1& \text{Uitwerken } \\ & =aq-1a-\frac{16}{15}q+\frac{16}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-1}{10}+b)(\frac{16}{20}+p)& =(\color{red}{b}+\color{orange}{\frac{-1}{10}}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{5}b-\frac{1}{10}p-\frac{1}{10}.\frac{4}{5}& \text{Uitwerken } \\ & =bp+\frac{4}{5}b-\frac{1}{10}p-\frac{4}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{4}{5}b-\frac{1}{10}p-\frac{2}{25} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-16}{14})(x-\frac{-18}{10})& =(\color{red}{a}+\color{orange}{\frac{-8}{7}}).(\color{green}{x}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{5}a-\frac{8}{7}x-\frac{8}{7}.\frac{9}{5}& \text{Uitwerken } \\ & =ax+\frac{9}{5}a-\frac{8}{7}x-\frac{72}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-30 10:17:14
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