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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-9)(\frac{-8}{12}-a)& =(\color{red}{q}+\color{orange}{(-9)}).(\color{green}{-a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-9)} . \color{green}{(-a)} + \color{orange}{(-9)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{2}{3}q+9a+9.\frac{2}{3}& \text{Uitwerken } \\ & =-aq-\frac{2}{3}q+9a+\frac{18}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{2}{3}q+9a+6 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-14}{6})(\frac{-6}{16}-b)& =(\color{red}{a}+\color{orange}{\frac{-7}{3}}).(\color{green}{-b}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{8}a+\frac{7}{3}b+\frac{7}{3}.\frac{3}{8}& \text{Uitwerken } \\ & =-ab-\frac{3}{8}a+\frac{7}{3}b+\frac{21}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{3}{8}a+\frac{7}{3}b+\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-20}{16})(\frac{12}{13}-x)& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{-x}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{12}{13}p+\frac{5}{4}x-\frac{5}{4}.\frac{12}{13}& \text{Uitwerken } \\ & =-px+\frac{12}{13}p+\frac{5}{4}x-\frac{60}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{12}{13}p+\frac{5}{4}x-\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{7}{20}-q)(1+a)& =(\color{red}{-q}+\color{orange}{\frac{7}{20}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{20})} . \color{green}{(a)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aq-1q+\frac{7}{20}a+\frac{7}{20}.1& \text{Uitwerken } \\ & =-aq-1q+\frac{7}{20}a+\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{17}{18})(\frac{-11}{3}+q)& =(\color{red}{a}+\color{orange}{\frac{-17}{18}}).(\color{green}{q}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{3}a-\frac{17}{18}q+\frac{17}{18}.\frac{11}{3}& \text{Uitwerken } \\ & =aq-\frac{11}{3}a-\frac{17}{18}q+\frac{187}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-11}{5})(p-\frac{15}{16})& =(\color{red}{q}+\color{orange}{\frac{-11}{5}}).(\color{green}{p}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{15}{16}q-\frac{11}{5}p+\frac{11}{5}.\frac{15}{16}& \text{Uitwerken } \\ & =pq-\frac{15}{16}q-\frac{11}{5}p+\frac{165}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{15}{16}q-\frac{11}{5}p+\frac{33}{16} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{10}{14}-q)(2+x)& =(\color{red}{-q}+\color{orange}{\frac{5}{7}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{5}{7})} . \color{green}{(x)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qx-2q+\frac{5}{7}x+\frac{5}{7}.2& \text{Uitwerken } \\ & =-qx-2q+\frac{5}{7}x+\frac{10}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{9}{3}-p)(\frac{9}{15}-q)& =(\color{red}{-p}+\color{orange}{3}).(\color{green}{-q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(3)} . \color{green}{(-q)} + \color{orange}{(3)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{5}p-3q+3.\frac{3}{5}& \text{Uitwerken } \\ & =pq-\frac{3}{5}p-3q+\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-5}{9}+b)(b-\frac{-10}{18})& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{9}b-\frac{5}{9}b-\frac{5}{9}.\frac{5}{9}& \text{Uitwerken } \\ & =b^2+(\frac{5}{9}+(\frac{-5}{9}))b-(\frac{-25}{81}) & \text{Neem samen} \\ &=b^2+\frac{0}{9}b-(\frac{-25}{81}) & \text{Maak de som} \\ &=b^2+0b+\frac{25}{81} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(\frac{-11}{18}+q)(p+\frac{-2}{13})& =(\color{red}{q}+\color{orange}{\frac{-11}{18}}).(\color{green}{p}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{13}q-\frac{11}{18}p+\frac{11}{18}.\frac{2}{13}& \text{Uitwerken } \\ & =pq-\frac{2}{13}q-\frac{11}{18}p+\frac{22}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{2}{13}q-\frac{11}{18}p+\frac{11}{117} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{8}{7}+b)(b-\frac{5}{10})& =(\color{red}{b}+\color{orange}{\frac{8}{7}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{8}{7})} . \color{green}{(b)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{2}b+\frac{8}{7}b-\frac{8}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{2})+\frac{8}{7})b-(\frac{-8}{14}) & \text{Neem samen} \\ &=b^2+\frac{9}{14}b-(\frac{-8}{14}) & \text{Maak de som} \\ &=b^2+\frac{9}{14}b+\frac{4}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{5}{5}-q)(\frac{-14}{7}-p)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(-2)} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq+2q-1p-1.2& \text{Uitwerken } \\ & =pq+2q-1p-2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-22 20:04:12
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