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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-16}{5})(b-\frac{-3}{17})& =(\color{red}{p}+\color{orange}{\frac{-16}{5}}).(\color{green}{b}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{17}p-\frac{16}{5}b-\frac{16}{5}.\frac{3}{17}& \text{Uitwerken } \\ & =bp+\frac{3}{17}p-\frac{16}{5}b-\frac{48}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-7}{9})(a-\frac{-17}{15})& =(\color{red}{b}+\color{orange}{\frac{7}{9}}).(\color{green}{a}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(\frac{7}{9})} . \color{green}{(a)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{15}b+\frac{7}{9}a+\frac{7}{9}.\frac{17}{15}& \text{Uitwerken } \\ & =ab+\frac{17}{15}b+\frac{7}{9}a+\frac{119}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-13}{14}+p)(\frac{15}{4}+q)& =(\color{red}{p}+\color{orange}{\frac{-13}{14}}).(\color{green}{q}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{15}{4}p-\frac{13}{14}q-\frac{13}{14}.\frac{15}{4}& \text{Uitwerken } \\ & =pq+\frac{15}{4}p-\frac{13}{14}q-\frac{195}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{12}{13})(b-\frac{-3}{2})& =(\color{red}{a}+\color{orange}{\frac{12}{13}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{12}{13})} . \color{green}{(b)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{2}a+\frac{12}{13}b+\frac{12}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =ab+\frac{3}{2}a+\frac{12}{13}b+\frac{36}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{2}a+\frac{12}{13}b+\frac{18}{13} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{1}{9})(p+\frac{2}{10})& =(\color{red}{a}+\color{orange}{\frac{-1}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{5}a-\frac{1}{9}p-\frac{1}{9}.\frac{1}{5}& \text{Uitwerken } \\ & =ap+\frac{1}{5}a-\frac{1}{9}p-\frac{1}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{7}{13})(\frac{-18}{5}+p)& =(\color{red}{a}+\color{orange}{\frac{-7}{13}}).(\color{green}{p}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{18}{5}a-\frac{7}{13}p+\frac{7}{13}.\frac{18}{5}& \text{Uitwerken } \\ & =ap-\frac{18}{5}a-\frac{7}{13}p+\frac{126}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{19}{19})(\frac{-5}{3}-p)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{5}{3}p+1p+1.\frac{5}{3}& \text{Uitwerken } \\ & =-p^2+((\frac{-5}{3})+1)p+(\frac{-5}{3}) & \text{Neem samen} \\ &=-p^2-\frac{2}{3}p+(\frac{-5}{3}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(b-\frac{18}{12})(x+\frac{7}{13})& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{x}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{13}b-\frac{3}{2}x-\frac{3}{2}.\frac{7}{13}& \text{Uitwerken } \\ & =bx+\frac{7}{13}b-\frac{3}{2}x-\frac{21}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-7}{20})(\frac{20}{11}+q)& =(\color{red}{p}+\color{orange}{\frac{-7}{20}}).(\color{green}{q}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{20}{11}p-\frac{7}{20}q-\frac{7}{20}.\frac{20}{11}& \text{Uitwerken } \\ & =pq+\frac{20}{11}p-\frac{7}{20}q-\frac{140}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{20}{11}p-\frac{7}{20}q-\frac{7}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-14}{4}-q)(\frac{20}{9}-b)& =(\color{red}{-q}+\color{orange}{\frac{-7}{2}}).(\color{green}{-b}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{20}{9}q+\frac{7}{2}b-\frac{7}{2}.\frac{20}{9}& \text{Uitwerken } \\ & =bq-\frac{20}{9}q+\frac{7}{2}b-\frac{140}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{20}{9}q+\frac{7}{2}b-\frac{70}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{6}+a)(\frac{8}{20}+b)& =(\color{red}{a}+\color{orange}{\frac{11}{6}}).(\color{green}{b}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{11}{6})} . \color{green}{(b)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{5}a+\frac{11}{6}b+\frac{11}{6}.\frac{2}{5}& \text{Uitwerken } \\ & =ab+\frac{2}{5}a+\frac{11}{6}b+\frac{22}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{2}{5}a+\frac{11}{6}b+\frac{11}{15} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{17}-x)(\frac{-3}{19}-b)& =(\color{red}{-x}+\color{orange}{\frac{9}{17}}).(\color{green}{-b}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{9}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{19}x-\frac{9}{17}b-\frac{9}{17}.\frac{3}{19}& \text{Uitwerken } \\ & =bx+\frac{3}{19}x-\frac{9}{17}b-\frac{27}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-11-21 04:14:55
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