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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{20}-x)(x-\frac{-15}{15})& =(\color{red}{-x}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -xx-1x+\frac{3}{4}x+\frac{3}{4}.1& \text{Uitwerken } \\ & =-x^2+((-1)+\frac{3}{4})x+(\frac{-3}{4}) & \text{Neem samen} \\ &=-x^2-\frac{1}{4}x+(\frac{-3}{4}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{13}{12}-b)(\frac{-11}{9}-x)& =(\color{red}{-b}+\color{orange}{\frac{13}{12}}).(\color{green}{-x}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{13}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{9}b-\frac{13}{12}x-\frac{13}{12}.\frac{11}{9}& \text{Uitwerken } \\ & =bx+\frac{11}{9}b-\frac{13}{12}x-\frac{143}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-12}{14})(\frac{17}{4}-p)& =(\color{red}{x}+\color{orange}{\frac{-6}{7}}).(\color{green}{-p}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{17}{4}x+\frac{6}{7}p-\frac{6}{7}.\frac{17}{4}& \text{Uitwerken } \\ & =-px+\frac{17}{4}x+\frac{6}{7}p-\frac{102}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{17}{4}x+\frac{6}{7}p-\frac{51}{14} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{17}{18})(\frac{12}{16}-p)& =(\color{red}{p}+\color{orange}{\frac{-17}{18}}).(\color{green}{-p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{3}{4}p+\frac{17}{18}p-\frac{17}{18}.\frac{3}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{3}{4}+\frac{17}{18})p-\frac{51}{72} & \text{Neem samen} \\ &=-p^2+\frac{61}{36}p-\frac{51}{72} & \text{Maak de som} \\ &=-p^2+\frac{61}{36}p-\frac{17}{24} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{7}{17}+q)(\frac{14}{11}+q)& =(\color{red}{q}+\color{orange}{\frac{7}{17}}).(\color{green}{q}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{7}{17})} . \color{green}{(q)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{14}{11}q+\frac{7}{17}q+\frac{7}{17}.\frac{14}{11}& \text{Uitwerken } \\ & =q^2+(\frac{14}{11}+\frac{7}{17})q+\frac{98}{187} & \text{Neem samen} \\ &=q^2+\frac{315}{187}q+\frac{98}{187} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-15}{7})(\frac{9}{10}+b)& =(\color{red}{a}+\color{orange}{\frac{-15}{7}}).(\color{green}{b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{10}a-\frac{15}{7}b-\frac{15}{7}.\frac{9}{10}& \text{Uitwerken } \\ & =ab+\frac{9}{10}a-\frac{15}{7}b-\frac{135}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{9}{10}a-\frac{15}{7}b-\frac{27}{14} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{7}+b)(\frac{12}{11}-p)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{12}{11}b+2p-2.\frac{12}{11}& \text{Uitwerken } \\ & =-bp+\frac{12}{11}b+2p-\frac{24}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-9}{12})(q+\frac{8}{14})& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{7}x-\frac{3}{4}q-\frac{3}{4}.\frac{4}{7}& \text{Uitwerken } \\ & =qx+\frac{4}{7}x-\frac{3}{4}q-\frac{12}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{4}{7}x-\frac{3}{4}q-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{10}{5}+p)(\frac{-16}{11}-a)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-a}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(2)} . \color{green}{(-a)} + \color{orange}{(2)} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{16}{11}p-2a-2.\frac{16}{11}& \text{Uitwerken } \\ & =-ap-\frac{16}{11}p-2a-\frac{32}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{-16}{16})(\frac{-20}{18}+p)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{9}x-1p+1.\frac{10}{9}& \text{Uitwerken } \\ & =px-\frac{10}{9}x-1p+\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-13}{16})(\frac{14}{8}-q)& =(\color{red}{p}+\color{orange}{\frac{-13}{16}}).(\color{green}{-q}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{7}{4}p+\frac{13}{16}q-\frac{13}{16}.\frac{7}{4}& \text{Uitwerken } \\ & =-pq+\frac{7}{4}p+\frac{13}{16}q-\frac{91}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{12}{5})(\frac{-18}{20}-q)& =(\color{red}{a}+\color{orange}{\frac{12}{5}}).(\color{green}{-q}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{12}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{10}a-\frac{12}{5}q-\frac{12}{5}.\frac{9}{10}& \text{Uitwerken } \\ & =-aq-\frac{9}{10}a-\frac{12}{5}q-\frac{108}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{9}{10}a-\frac{12}{5}q-\frac{54}{25} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-07-14 23:22:11
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