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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-12}{2})(\frac{-1}{14}-x)& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{-x}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(-6)} . \color{green}{(-x)} + \color{orange}{(-6)} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{14}a+6x+6.\frac{1}{14}& \text{Uitwerken } \\ & =-ax-\frac{1}{14}a+6x+\frac{6}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{1}{14}a+6x+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{18}{10}+x)(p+\frac{18}{13})& =(\color{red}{x}+\color{orange}{\frac{9}{5}}).(\color{green}{p}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{9}{5})} . \color{green}{(p)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{18}{13}x+\frac{9}{5}p+\frac{9}{5}.\frac{18}{13}& \text{Uitwerken } \\ & =px+\frac{18}{13}x+\frac{9}{5}p+\frac{162}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-16}{2})(\frac{17}{16}+p)& =(\color{red}{p}+\color{orange}{8}).(\color{green}{p}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(8)} . \color{green}{(p)} + \color{orange}{(8)} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{16}p+8p+8.\frac{17}{16}& \text{Uitwerken } \\ & =p^2+(\frac{17}{16}+8)p+\frac{136}{16} & \text{Neem samen} \\ &=p^2+\frac{145}{16}p+\frac{136}{16} & \text{Maak de som} \\ &=p^2+\frac{145}{16}p+\frac{17}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{3}{2}-a)(b-\frac{4}{5})& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{4}{5}a+\frac{3}{2}b-\frac{3}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =-ab+\frac{4}{5}a+\frac{3}{2}b-\frac{12}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{4}{5}a+\frac{3}{2}b-\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-8}{17}+x)(\frac{-16}{17}+q)& =(\color{red}{x}+\color{orange}{\frac{-8}{17}}).(\color{green}{q}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{17}x-\frac{8}{17}q+\frac{8}{17}.\frac{16}{17}& \text{Uitwerken } \\ & =qx-\frac{16}{17}x-\frac{8}{17}q+\frac{128}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{5}-q)(\frac{-20}{7}+x)& =(\color{red}{-q}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{20}{7}q-\frac{4}{5}x+\frac{4}{5}.\frac{20}{7}& \text{Uitwerken } \\ & =-qx+\frac{20}{7}q-\frac{4}{5}x+\frac{80}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{20}{7}q-\frac{4}{5}x+\frac{16}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+\frac{18}{18})(q+\frac{-1}{9})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{9}p+1q-1.\frac{1}{9}& \text{Uitwerken } \\ & =pq-\frac{1}{9}p+1q-\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{4}{9})(x+\frac{-15}{5})& =(\color{red}{a}+\color{orange}{\frac{4}{9}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ax-3a+\frac{4}{9}x-\frac{4}{9}.3& \text{Uitwerken } \\ & =ax-3a+\frac{4}{9}x-\frac{12}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-3a+\frac{4}{9}x-\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a-\frac{15}{12})(\frac{-19}{2}-b)& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{-b}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{19}{2}a+\frac{5}{4}b+\frac{5}{4}.\frac{19}{2}& \text{Uitwerken } \\ & =-ab-\frac{19}{2}a+\frac{5}{4}b+\frac{95}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{1}{19})(\frac{-19}{5}-q)& =(\color{red}{q}+\color{orange}{\frac{-1}{19}}).(\color{green}{-q}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{-1}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{19}{5}q+\frac{1}{19}q+\frac{1}{19}.\frac{19}{5}& \text{Uitwerken } \\ & =-q^2+((\frac{-19}{5})+\frac{1}{19})q+(\frac{-19}{95}) & \text{Neem samen} \\ &=-q^2-\frac{356}{95}q+(\frac{-19}{95}) & \text{Maak de som} \\ &=-q^2-\frac{356}{95}q+(\frac{-1}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{10}-p)(b+\frac{-19}{13})& =(\color{red}{-p}+\color{orange}{\frac{-7}{5}}).(\color{green}{b}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{13}p-\frac{7}{5}b+\frac{7}{5}.\frac{19}{13}& \text{Uitwerken } \\ & =-bp+\frac{19}{13}p-\frac{7}{5}b+\frac{133}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{6}{11}-b)(a-\frac{12}{6})& =(\color{red}{-b}+\color{orange}{\frac{6}{11}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(-2)} + \color{orange}{(\frac{6}{11})} . \color{green}{(a)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ab+2b+\frac{6}{11}a-\frac{6}{11}.2& \text{Uitwerken } \\ & =-ab+2b+\frac{6}{11}a-\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-30 01:15:51
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