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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-8}{14}+a)(\frac{2}{19}-x)& =(\color{red}{a}+\color{orange}{\frac{-4}{7}}).(\color{green}{-x}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{19}a+\frac{4}{7}x-\frac{4}{7}.\frac{2}{19}& \text{Uitwerken } \\ & =-ax+\frac{2}{19}a+\frac{4}{7}x-\frac{8}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-14}{13})(p+\frac{-14}{13})& =(\color{red}{a}+\color{orange}{\frac{-14}{13}}).(\color{green}{p}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{14}{13}a-\frac{14}{13}p+\frac{14}{13}.\frac{14}{13}& \text{Uitwerken } \\ & =ap-\frac{14}{13}a-\frac{14}{13}p+\frac{196}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-12}{6})(a+\frac{-12}{7})& =(\color{red}{b}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-12}{7})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{12}{7}b+2a-2.\frac{12}{7}& \text{Uitwerken } \\ & =ab-\frac{12}{7}b+2a-\frac{24}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-15}{18})(q+\frac{6}{8})& =(\color{red}{a}+\color{orange}{\frac{-5}{6}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{4}a-\frac{5}{6}q-\frac{5}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =aq+\frac{3}{4}a-\frac{5}{6}q-\frac{15}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{4}a-\frac{5}{6}q-\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-2}{6})(\frac{-1}{17}+p)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{17}x+\frac{1}{3}p-\frac{1}{3}.\frac{1}{17}& \text{Uitwerken } \\ & =px-\frac{1}{17}x+\frac{1}{3}p-\frac{1}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-8}{5})(\frac{-1}{20}-p)& =(\color{red}{p}+\color{orange}{\frac{-8}{5}}).(\color{green}{-p}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{20}p+\frac{8}{5}p+\frac{8}{5}.\frac{1}{20}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{20})+\frac{8}{5})p+(\frac{-8}{100}) & \text{Neem samen} \\ &=-p^2+\frac{31}{20}p+(\frac{-8}{100}) & \text{Maak de som} \\ &=-p^2+\frac{31}{20}p+(\frac{-2}{25}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(q+\frac{5}{4})(b+\frac{4}{14})& =(\color{red}{q}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{7}q+\frac{5}{4}b+\frac{5}{4}.\frac{2}{7}& \text{Uitwerken } \\ & =bq+\frac{2}{7}q+\frac{5}{4}b+\frac{10}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{2}{7}q+\frac{5}{4}b+\frac{5}{14} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{11}+p)(\frac{-17}{2}-x)& =(\color{red}{p}+\color{orange}{\frac{4}{11}}).(\color{green}{-x}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{4}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{17}{2}p-\frac{4}{11}x-\frac{4}{11}.\frac{17}{2}& \text{Uitwerken } \\ & =-px-\frac{17}{2}p-\frac{4}{11}x-\frac{68}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{17}{2}p-\frac{4}{11}x-\frac{34}{11} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{19}{2})(\frac{-2}{17}-b)& =(\color{red}{x}+\color{orange}{\frac{-19}{2}}).(\color{green}{-b}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{2}{17}x+\frac{19}{2}b+\frac{19}{2}.\frac{2}{17}& \text{Uitwerken } \\ & =-bx-\frac{2}{17}x+\frac{19}{2}b+\frac{38}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{2}{17}x+\frac{19}{2}b+\frac{19}{17} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{4}+x)(\frac{9}{16}-x)& =(\color{red}{x}+\color{orange}{4}).(\color{green}{-x}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(4)} . \color{green}{(-x)} + \color{orange}{(4)} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{9}{16}x-4x+4.\frac{9}{16}& \text{Uitwerken } \\ & =-x^2+(\frac{9}{16}+(-4))x+(\frac{-36}{16}) & \text{Neem samen} \\ &=-x^2-\frac{55}{16}x+(\frac{-36}{16}) & \text{Maak de som} \\ &=-x^2-\frac{55}{16}x+(\frac{-9}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(a+\frac{1}{5})(\frac{6}{9}-a)& =(\color{red}{a}+\color{orange}{\frac{1}{5}}).(\color{green}{-a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{2}{3}a-\frac{1}{5}a+\frac{1}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =-a^2+(\frac{2}{3}+(\frac{-1}{5}))a+(\frac{-2}{15}) & \text{Neem samen} \\ &=-a^2+\frac{7}{15}a+(\frac{-2}{15}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-10}{2})(b-\frac{15}{16})& =(\color{red}{a}+\color{orange}{5}).(\color{green}{b}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(5)} . \color{green}{(b)} + \color{orange}{(5)} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{16}a+5b-5.\frac{15}{16}& \text{Uitwerken } \\ & =ab-\frac{15}{16}a+5b-\frac{75}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-20 20:42:43
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