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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{10}-a)(\frac{-14}{10}+q)& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{5}a+\frac{3}{2}q-\frac{3}{2}.\frac{7}{5}& \text{Uitwerken } \\ & =-aq+\frac{7}{5}a+\frac{3}{2}q-\frac{21}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{14}{12}+b)(q+\frac{6}{19})& =(\color{red}{b}+\color{orange}{\frac{7}{6}}).(\color{green}{q}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{7}{6})} . \color{green}{(q)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{6}{19}b+\frac{7}{6}q+\frac{7}{6}.\frac{6}{19}& \text{Uitwerken } \\ & =bq+\frac{6}{19}b+\frac{7}{6}q+\frac{42}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{6}{19}b+\frac{7}{6}q+\frac{7}{19} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-10}{4}+q)(\frac{-20}{7}-q)& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{-q}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{20}{7}q+\frac{5}{2}q+\frac{5}{2}.\frac{20}{7}& \text{Uitwerken } \\ & =-q^2+((\frac{-20}{7})+\frac{5}{2})q+(\frac{-100}{14}) & \text{Neem samen} \\ &=-q^2-\frac{5}{14}q+(\frac{-100}{14}) & \text{Maak de som} \\ &=-q^2-\frac{5}{14}q+(\frac{-50}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-6}{11})(\frac{-16}{15}+x)& =(\color{red}{x}+\color{orange}{\frac{6}{11}}).(\color{green}{x}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(\frac{6}{11})} . \color{green}{(x)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{16}{15}x+\frac{6}{11}x-\frac{6}{11}.\frac{16}{15}& \text{Uitwerken } \\ & =x^2+((\frac{-16}{15})+\frac{6}{11})x-(\frac{-96}{165}) & \text{Neem samen} \\ &=x^2-\frac{86}{165}x-(\frac{-96}{165}) & \text{Maak de som} \\ &=x^2-\frac{86}{165}x+\frac{32}{55} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(x-\frac{2}{18})(\frac{-8}{10}-a)& =(\color{red}{x}+\color{orange}{\frac{-1}{9}}).(\color{green}{-a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{4}{5}x+\frac{1}{9}a+\frac{1}{9}.\frac{4}{5}& \text{Uitwerken } \\ & =-ax-\frac{4}{5}x+\frac{1}{9}a+\frac{4}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{2}{7}+a)(\frac{13}{9}-p)& =(\color{red}{a}+\color{orange}{\frac{2}{7}}).(\color{green}{-p}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{2}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{9}a-\frac{2}{7}p+\frac{2}{7}.\frac{13}{9}& \text{Uitwerken } \\ & =-ap+\frac{13}{9}a-\frac{2}{7}p+\frac{26}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-6}{10})(\frac{13}{9}-x)& =(\color{red}{x}+\color{orange}{\frac{3}{5}}).(\color{green}{-x}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{13}{9}x-\frac{3}{5}x+\frac{3}{5}.\frac{13}{9}& \text{Uitwerken } \\ & =-x^2+(\frac{13}{9}+(\frac{-3}{5}))x+(\frac{-39}{45}) & \text{Neem samen} \\ &=-x^2+\frac{38}{45}x+(\frac{-39}{45}) & \text{Maak de som} \\ &=-x^2+\frac{38}{45}x+(\frac{-13}{15}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-1}{13}-b)(b-\frac{12}{4})& =(\color{red}{-b}+\color{orange}{\frac{-1}{13}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bb+3b-\frac{1}{13}b+\frac{1}{13}.3& \text{Uitwerken } \\ & =-b^2+(3+(\frac{-1}{13}))b+(\frac{-3}{13}) & \text{Neem samen} \\ &=-b^2+\frac{38}{13}b+(\frac{-3}{13}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-14}{9})(\frac{-20}{20}+a)& =(\color{red}{a}+\color{orange}{\frac{-14}{9}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-14}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aa-1a-\frac{14}{9}a+\frac{14}{9}.1& \text{Uitwerken } \\ & =a^2+((-1)+(\frac{-14}{9}))a+\frac{14}{9} & \text{Neem samen} \\ &=a^2-\frac{23}{9}a+\frac{14}{9} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(a+\frac{3}{10})((-15)-p)& =(\color{red}{a}+\color{orange}{\frac{3}{10}}).(\color{green}{-p}+\color{blue}{(-15)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-15)} + \color{orange}{(\frac{3}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = -ap-15a-\frac{3}{10}p-\frac{3}{10}.15& \text{Uitwerken } \\ & =-ap-15a-\frac{3}{10}p-\frac{45}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-15a-\frac{3}{10}p-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-18}{4}-p)(\frac{9}{16}+q)& =(\color{red}{-p}+\color{orange}{\frac{-9}{2}}).(\color{green}{q}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{16}p-\frac{9}{2}q-\frac{9}{2}.\frac{9}{16}& \text{Uitwerken } \\ & =-pq-\frac{9}{16}p-\frac{9}{2}q-\frac{81}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-8}{8})(b+\frac{13}{17})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{17}p+1b+1.\frac{13}{17}& \text{Uitwerken } \\ & =bp+\frac{13}{17}p+1b+\frac{13}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-24 20:44:53
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