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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-2}{19})(b-\frac{-18}{5})& =(\color{red}{p}+\color{orange}{\frac{-2}{19}}).(\color{green}{b}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{18}{5}p-\frac{2}{19}b-\frac{2}{19}.\frac{18}{5}& \text{Uitwerken } \\ & =bp+\frac{18}{5}p-\frac{2}{19}b-\frac{36}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{5}-a)(a+\frac{3}{20})& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{3}{20}a-2a-2.\frac{3}{20}& \text{Uitwerken } \\ & =-a^2+((\frac{-3}{20})+(-2))a-\frac{6}{20} & \text{Neem samen} \\ &=-a^2-\frac{43}{20}a-\frac{6}{20} & \text{Maak de som} \\ &=-a^2-\frac{43}{20}a-\frac{3}{10} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-8}{11}+q)(\frac{4}{4}+x)& =(\color{red}{q}+\color{orange}{\frac{-8}{11}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{-8}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1q-\frac{8}{11}x-\frac{8}{11}.1& \text{Uitwerken } \\ & =qx+1q-\frac{8}{11}x-\frac{8}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{4}+x)(p-\frac{14}{11})& =(\color{red}{x}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{14}{11}x+5p-5.\frac{14}{11}& \text{Uitwerken } \\ & =px-\frac{14}{11}x+5p-\frac{70}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-4}{13}-x)(\frac{6}{5}-q)& =(\color{red}{-x}+\color{orange}{\frac{-4}{13}}).(\color{green}{-q}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{6}{5}x+\frac{4}{13}q-\frac{4}{13}.\frac{6}{5}& \text{Uitwerken } \\ & =qx-\frac{6}{5}x+\frac{4}{13}q-\frac{24}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{16}{3})(\frac{16}{2}+q)& =(\color{red}{p}+\color{orange}{\frac{-16}{3}}).(\color{green}{q}+\color{blue}{8})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(8)} + \color{orange}{(\frac{-16}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = pq+8p-\frac{16}{3}q-\frac{16}{3}.8& \text{Uitwerken } \\ & =pq+8p-\frac{16}{3}q-\frac{128}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{14}+p)(x-\frac{-13}{4})& =(\color{red}{p}+\color{orange}{\frac{9}{14}}).(\color{green}{x}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{9}{14})} . \color{green}{(x)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{4}p+\frac{9}{14}x+\frac{9}{14}.\frac{13}{4}& \text{Uitwerken } \\ & =px+\frac{13}{4}p+\frac{9}{14}x+\frac{117}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-18}{17}+a)(\frac{-19}{11}-q)& =(\color{red}{a}+\color{orange}{\frac{-18}{17}}).(\color{green}{-q}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{11}a+\frac{18}{17}q+\frac{18}{17}.\frac{19}{11}& \text{Uitwerken } \\ & =-aq-\frac{19}{11}a+\frac{18}{17}q+\frac{342}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-14}{17}+a)(b+\frac{13}{11})& =(\color{red}{a}+\color{orange}{\frac{-14}{17}}).(\color{green}{b}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{11}a-\frac{14}{17}b-\frac{14}{17}.\frac{13}{11}& \text{Uitwerken } \\ & =ab+\frac{13}{11}a-\frac{14}{17}b-\frac{182}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-8}{18}+b)(\frac{-5}{10}+p)& =(\color{red}{b}+\color{orange}{\frac{-4}{9}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{2}b-\frac{4}{9}p+\frac{4}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =bp-\frac{1}{2}b-\frac{4}{9}p+\frac{4}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{1}{2}b-\frac{4}{9}p+\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{8}{3})((-15)-a)& =(\color{red}{q}+\color{orange}{\frac{8}{3}}).(\color{green}{-a}+\color{blue}{(-15)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-15)} + \color{orange}{(\frac{8}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = -aq-15q-\frac{8}{3}a-\frac{8}{3}.15& \text{Uitwerken } \\ & =-aq-15q-\frac{8}{3}a-\frac{120}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-15q-\frac{8}{3}a-40 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x+\frac{12}{11})(a+\frac{9}{12})& =(\color{red}{x}+\color{orange}{\frac{12}{11}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{12}{11})} . \color{green}{(a)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{4}x+\frac{12}{11}a+\frac{12}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =ax+\frac{3}{4}x+\frac{12}{11}a+\frac{36}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{4}x+\frac{12}{11}a+\frac{9}{11} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-11 11:18:44
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