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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{2}+q)(\frac{-9}{14}-x)& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{-x}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(-3)} . \color{green}{(-x)} + \color{orange}{(-3)} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{9}{14}q+3x+3.\frac{9}{14}& \text{Uitwerken } \\ & =-qx-\frac{9}{14}q+3x+\frac{27}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{1}{11})(\frac{-6}{2}-q)& =(\color{red}{b}+\color{orange}{\frac{-1}{11}}).(\color{green}{-q}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bq-3b+\frac{1}{11}q+\frac{1}{11}.3& \text{Uitwerken } \\ & =-bq-3b+\frac{1}{11}q+\frac{3}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{12}{17}+p)(a-\frac{-6}{9})& =(\color{red}{p}+\color{orange}{\frac{12}{17}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{3}p+\frac{12}{17}a+\frac{12}{17}.\frac{2}{3}& \text{Uitwerken } \\ & =ap+\frac{2}{3}p+\frac{12}{17}a+\frac{24}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{2}{3}p+\frac{12}{17}a+\frac{8}{17} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-12}{20})(q-\frac{8}{9})& =(\color{red}{x}+\color{orange}{\frac{-3}{5}}).(\color{green}{q}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{9}x-\frac{3}{5}q+\frac{3}{5}.\frac{8}{9}& \text{Uitwerken } \\ & =qx-\frac{8}{9}x-\frac{3}{5}q+\frac{24}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{8}{9}x-\frac{3}{5}q+\frac{8}{15} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-19}{7})(x-\frac{-13}{18})& =(\color{red}{a}+\color{orange}{\frac{-19}{7}}).(\color{green}{x}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{13}{18}a-\frac{19}{7}x-\frac{19}{7}.\frac{13}{18}& \text{Uitwerken } \\ & =ax+\frac{13}{18}a-\frac{19}{7}x-\frac{247}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-2}{4})(10-x)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{-x}+\color{blue}{10})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(10)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -px+10p+\frac{1}{2}x-\frac{1}{2}.10& \text{Uitwerken } \\ & =-px+10p+\frac{1}{2}x-\frac{10}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+10p+\frac{1}{2}x-5 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{20}-x)(q-\frac{12}{19})& =(\color{red}{-x}+\color{orange}{\frac{-7}{10}}).(\color{green}{q}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{12}{19}x-\frac{7}{10}q+\frac{7}{10}.\frac{12}{19}& \text{Uitwerken } \\ & =-qx+\frac{12}{19}x-\frac{7}{10}q+\frac{84}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{12}{19}x-\frac{7}{10}q+\frac{42}{95} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-12}{3})(b+\frac{15}{19})& =(\color{red}{b}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{15}{19}b-4b-4.\frac{15}{19}& \text{Uitwerken } \\ & =b^2+(\frac{15}{19}+(-4))b-(\frac{-60}{19}) & \text{Neem samen} \\ &=b^2-\frac{61}{19}b-(\frac{-60}{19}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{20}{19}+q)(\frac{-1}{7}-a)& =(\color{red}{q}+\color{orange}{\frac{20}{19}}).(\color{green}{-a}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{20}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{7}q-\frac{20}{19}a-\frac{20}{19}.\frac{1}{7}& \text{Uitwerken } \\ & =-aq-\frac{1}{7}q-\frac{20}{19}a-\frac{20}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-18}{4}-q)(p-\frac{-15}{3})& =(\color{red}{-q}+\color{orange}{\frac{-9}{2}}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(5)} + \color{orange}{(\frac{-9}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -pq-5q-\frac{9}{2}p-\frac{9}{2}.5& \text{Uitwerken } \\ & =-pq-5q-\frac{9}{2}p-\frac{45}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{13}-p)(\frac{-5}{9}+p)& =(\color{red}{-p}+\color{orange}{\frac{-3}{13}}).(\color{green}{p}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{5}{9}p-\frac{3}{13}p+\frac{3}{13}.\frac{5}{9}& \text{Uitwerken } \\ & =-p^2+(\frac{5}{9}+(\frac{-3}{13}))p+(\frac{-15}{117}) & \text{Neem samen} \\ &=-p^2+\frac{38}{117}p+(\frac{-15}{117}) & \text{Maak de som} \\ &=-p^2+\frac{38}{117}p+(\frac{-5}{39}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{-7}{11}+a)(\frac{8}{2}-x)& =(\color{red}{a}+\color{orange}{\frac{-7}{11}}).(\color{green}{-x}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{-7}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -ax+4a+\frac{7}{11}x-\frac{7}{11}.4& \text{Uitwerken } \\ & =-ax+4a+\frac{7}{11}x-\frac{28}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-15 15:33:55
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