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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{2}{2}+b)(\frac{5}{9}-q)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{9}b-1q+1.\frac{5}{9}& \text{Uitwerken } \\ & =-bq+\frac{5}{9}b-1q+\frac{5}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-8}{7}-q)(p-(-2))& =(\color{red}{-q}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -pq-2q-\frac{8}{7}p-\frac{8}{7}.2& \text{Uitwerken } \\ & =-pq-2q-\frac{8}{7}p-\frac{16}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{11}{3})(x+\frac{3}{8})& =(\color{red}{b}+\color{orange}{\frac{-11}{3}}).(\color{green}{x}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{8}b-\frac{11}{3}x-\frac{11}{3}.\frac{3}{8}& \text{Uitwerken } \\ & =bx+\frac{3}{8}b-\frac{11}{3}x-\frac{33}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{8}b-\frac{11}{3}x-\frac{11}{8} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-17}{9}-p)(\frac{-5}{14}+q)& =(\color{red}{-p}+\color{orange}{\frac{-17}{9}}).(\color{green}{q}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{14}p-\frac{17}{9}q+\frac{17}{9}.\frac{5}{14}& \text{Uitwerken } \\ & =-pq+\frac{5}{14}p-\frac{17}{9}q+\frac{85}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{13}+b)(b+\frac{13}{5})& =(\color{red}{b}+\color{orange}{\frac{-6}{13}}).(\color{green}{b}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{13}{5}b-\frac{6}{13}b-\frac{6}{13}.\frac{13}{5}& \text{Uitwerken } \\ & =b^2+(\frac{13}{5}+(\frac{-6}{13}))b-(\frac{-78}{65}) & \text{Neem samen} \\ &=b^2+\frac{139}{65}b-(\frac{-78}{65}) & \text{Maak de som} \\ &=b^2+\frac{139}{65}b+\frac{6}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(b-\frac{16}{19})(\frac{-14}{4}-q)& =(\color{red}{b}+\color{orange}{\frac{-16}{19}}).(\color{green}{-q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{2}b+\frac{16}{19}q+\frac{16}{19}.\frac{7}{2}& \text{Uitwerken } \\ & =-bq-\frac{7}{2}b+\frac{16}{19}q+\frac{112}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{7}{2}b+\frac{16}{19}q+\frac{56}{19} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-11}{6})(x-\frac{14}{14})& =(\color{red}{p}+\color{orange}{\frac{11}{6}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{11}{6})} . \color{green}{(x)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p+\frac{11}{6}x-\frac{11}{6}.1& \text{Uitwerken } \\ & =px-1p+\frac{11}{6}x-\frac{11}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+(-20))(\frac{6}{19}+p)& =(\color{red}{q}+\color{orange}{(-20)}).(\color{green}{p}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(-20)} . \color{green}{(p)} + \color{orange}{(-20)} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{6}{19}q-20p-20.\frac{6}{19}& \text{Uitwerken } \\ & =pq+\frac{6}{19}q-20p-\frac{120}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-10}{9}-p)(\frac{-8}{9}+q)& =(\color{red}{-p}+\color{orange}{\frac{-10}{9}}).(\color{green}{q}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{8}{9}p-\frac{10}{9}q+\frac{10}{9}.\frac{8}{9}& \text{Uitwerken } \\ & =-pq+\frac{8}{9}p-\frac{10}{9}q+\frac{80}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-17}{8}-a)(\frac{-16}{17}+q)& =(\color{red}{-a}+\color{orange}{\frac{-17}{8}}).(\color{green}{q}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{-17}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{16}{17}a-\frac{17}{8}q+\frac{17}{8}.\frac{16}{17}& \text{Uitwerken } \\ & =-aq+\frac{16}{17}a-\frac{17}{8}q+\frac{272}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{16}{17}a-\frac{17}{8}q+2 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{20}{11}-x)(b-\frac{-5}{2})& =(\color{red}{-x}+\color{orange}{\frac{20}{11}}).(\color{green}{b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{20}{11})} . \color{green}{(b)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{2}x+\frac{20}{11}b+\frac{20}{11}.\frac{5}{2}& \text{Uitwerken } \\ & =-bx-\frac{5}{2}x+\frac{20}{11}b+\frac{100}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{5}{2}x+\frac{20}{11}b+\frac{50}{11} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p-\frac{19}{18})(q-\frac{5}{12})& =(\color{red}{p}+\color{orange}{\frac{-19}{18}}).(\color{green}{q}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{12}p-\frac{19}{18}q+\frac{19}{18}.\frac{5}{12}& \text{Uitwerken } \\ & =pq-\frac{5}{12}p-\frac{19}{18}q+\frac{95}{216} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-23 20:46:37
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