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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{18}-a)(p-\frac{19}{12})& =(\color{red}{-a}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{12}a+\frac{5}{6}p-\frac{5}{6}.\frac{19}{12}& \text{Uitwerken } \\ & =-ap+\frac{19}{12}a+\frac{5}{6}p-\frac{95}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{10}{8})(b+\frac{7}{13})& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{13}p-\frac{5}{4}b-\frac{5}{4}.\frac{7}{13}& \text{Uitwerken } \\ & =bp+\frac{7}{13}p-\frac{5}{4}b-\frac{35}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{11}+x)(p-\frac{1}{5})& =(\color{red}{x}+\color{orange}{\frac{-7}{11}}).(\color{green}{p}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{5}x-\frac{7}{11}p+\frac{7}{11}.\frac{1}{5}& \text{Uitwerken } \\ & =px-\frac{1}{5}x-\frac{7}{11}p+\frac{7}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-10}{7}+b)(\frac{-6}{16}-x)& =(\color{red}{b}+\color{orange}{\frac{-10}{7}}).(\color{green}{-x}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{8}b+\frac{10}{7}x+\frac{10}{7}.\frac{3}{8}& \text{Uitwerken } \\ & =-bx-\frac{3}{8}b+\frac{10}{7}x+\frac{30}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{3}{8}b+\frac{10}{7}x+\frac{15}{28} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{11}{11})(x-\frac{-3}{13})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{13}a-1x-1.\frac{3}{13}& \text{Uitwerken } \\ & =ax+\frac{3}{13}a-1x-\frac{3}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{18}-x)(\frac{-9}{4}+a)& =(\color{red}{-x}+\color{orange}{\frac{-7}{18}}).(\color{green}{a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{4}x-\frac{7}{18}a+\frac{7}{18}.\frac{9}{4}& \text{Uitwerken } \\ & =-ax+\frac{9}{4}x-\frac{7}{18}a+\frac{63}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{9}{4}x-\frac{7}{18}a+\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{4}{3})(\frac{9}{13}-x)& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{-x}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{13}b-\frac{4}{3}x+\frac{4}{3}.\frac{9}{13}& \text{Uitwerken } \\ & =-bx+\frac{9}{13}b-\frac{4}{3}x+\frac{36}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{9}{13}b-\frac{4}{3}x+\frac{12}{13} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{6}{2}-b)(\frac{-14}{9}-x)& =(\color{red}{-b}+\color{orange}{3}).(\color{green}{-x}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(3)} . \color{green}{(-x)} + \color{orange}{(3)} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{14}{9}b-3x-3.\frac{14}{9}& \text{Uitwerken } \\ & =bx+\frac{14}{9}b-3x-\frac{42}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{14}{9}b-3x-\frac{14}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{10}{14})(\frac{-3}{8}+p)& =(\color{red}{b}+\color{orange}{\frac{-5}{7}}).(\color{green}{p}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{8}b-\frac{5}{7}p+\frac{5}{7}.\frac{3}{8}& \text{Uitwerken } \\ & =bp-\frac{3}{8}b-\frac{5}{7}p+\frac{15}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-14}{10}-a)(\frac{-8}{19}-q)& =(\color{red}{-a}+\color{orange}{\frac{-7}{5}}).(\color{green}{-q}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{19}a+\frac{7}{5}q+\frac{7}{5}.\frac{8}{19}& \text{Uitwerken } \\ & =aq+\frac{8}{19}a+\frac{7}{5}q+\frac{56}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-9}{17})(p+\frac{12}{16})& =(\color{red}{x}+\color{orange}{\frac{9}{17}}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{9}{17})} . \color{green}{(p)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{4}x+\frac{9}{17}p+\frac{9}{17}.\frac{3}{4}& \text{Uitwerken } \\ & =px+\frac{3}{4}x+\frac{9}{17}p+\frac{27}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{9}{17})(\frac{-20}{17}-b)& =(\color{red}{a}+\color{orange}{\frac{9}{17}}).(\color{green}{-b}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{9}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{20}{17}a-\frac{9}{17}b-\frac{9}{17}.\frac{20}{17}& \text{Uitwerken } \\ & =-ab-\frac{20}{17}a-\frac{9}{17}b-\frac{180}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-10 23:33:55
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