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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-12}{11})(\frac{-15}{4}+q)& =(\color{red}{a}+\color{orange}{\frac{12}{11}}).(\color{green}{q}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{12}{11})} . \color{green}{(q)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{4}a+\frac{12}{11}q-\frac{12}{11}.\frac{15}{4}& \text{Uitwerken } \\ & =aq-\frac{15}{4}a+\frac{12}{11}q-\frac{180}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{15}{4}a+\frac{12}{11}q-\frac{45}{11} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-9}{5}+q)(a-\frac{-20}{14})& =(\color{red}{q}+\color{orange}{\frac{-9}{5}}).(\color{green}{a}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{7}q-\frac{9}{5}a-\frac{9}{5}.\frac{10}{7}& \text{Uitwerken } \\ & =aq+\frac{10}{7}q-\frac{9}{5}a-\frac{90}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{10}{7}q-\frac{9}{5}a-\frac{18}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{9}+a)(\frac{-6}{16}-p)& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{-p}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{8}a-\frac{2}{3}p-\frac{2}{3}.\frac{3}{8}& \text{Uitwerken } \\ & =-ap-\frac{3}{8}a-\frac{2}{3}p-\frac{6}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{3}{8}a-\frac{2}{3}p-\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b-\frac{20}{10})(p+\frac{-12}{9})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{3}b-2p+2.\frac{4}{3}& \text{Uitwerken } \\ & =bp-\frac{4}{3}b-2p+\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{10}+a)(\frac{-9}{18}-q)& =(\color{red}{a}+\color{orange}{\frac{-1}{5}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{2}a+\frac{1}{5}q+\frac{1}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-aq-\frac{1}{2}a+\frac{1}{5}q+\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-11}{16})(\frac{-20}{17}+p)& =(\color{red}{p}+\color{orange}{\frac{-11}{16}}).(\color{green}{p}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{20}{17}p-\frac{11}{16}p+\frac{11}{16}.\frac{20}{17}& \text{Uitwerken } \\ & =p^2+((\frac{-20}{17})+(\frac{-11}{16}))p+\frac{220}{272} & \text{Neem samen} \\ &=p^2-\frac{507}{272}p+\frac{220}{272} & \text{Maak de som} \\ &=p^2-\frac{507}{272}p+\frac{55}{68} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-5}{6})(\frac{-15}{8}-x)& =(\color{red}{b}+\color{orange}{\frac{5}{6}}).(\color{green}{-x}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{15}{8}b-\frac{5}{6}x-\frac{5}{6}.\frac{15}{8}& \text{Uitwerken } \\ & =-bx-\frac{15}{8}b-\frac{5}{6}x-\frac{75}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{15}{8}b-\frac{5}{6}x-\frac{25}{16} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-16}{4})(p+\frac{17}{3})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{17}{3}q+4p+4.\frac{17}{3}& \text{Uitwerken } \\ & =pq+\frac{17}{3}q+4p+\frac{68}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-9}{20}-q)(x-\frac{-16}{15})& =(\color{red}{-q}+\color{orange}{\frac{-9}{20}}).(\color{green}{x}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{16}{15}q-\frac{9}{20}x-\frac{9}{20}.\frac{16}{15}& \text{Uitwerken } \\ & =-qx-\frac{16}{15}q-\frac{9}{20}x-\frac{144}{300} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{16}{15}q-\frac{9}{20}x-\frac{12}{25} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{9}{6}+x)(\frac{14}{18}+x)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{7}{9}x+\frac{3}{2}x+\frac{3}{2}.\frac{7}{9}& \text{Uitwerken } \\ & =x^2+(\frac{7}{9}+\frac{3}{2})x+\frac{21}{18} & \text{Neem samen} \\ &=x^2+\frac{41}{18}x+\frac{21}{18} & \text{Maak de som} \\ &=x^2+\frac{41}{18}x+\frac{7}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-5}{16})(\frac{11}{4}+x)& =(\color{red}{b}+\color{orange}{\frac{5}{16}}).(\color{green}{x}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{5}{16})} . \color{green}{(x)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{4}b+\frac{5}{16}x+\frac{5}{16}.\frac{11}{4}& \text{Uitwerken } \\ & =bx+\frac{11}{4}b+\frac{5}{16}x+\frac{55}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-10}{5})(p-\frac{16}{16})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a-2p+2.1& \text{Uitwerken } \\ & =ap-1a-2p+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-28 09:17:43
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