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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-20}{10}+b)(a+\frac{-9}{8})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{8}b-2a+2.\frac{9}{8}& \text{Uitwerken } \\ & =ab-\frac{9}{8}b-2a+\frac{18}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{9}{8}b-2a+\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x-\frac{8}{14})(\frac{20}{9}+b)& =(\color{red}{x}+\color{orange}{\frac{-4}{7}}).(\color{green}{b}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{20}{9}x-\frac{4}{7}b-\frac{4}{7}.\frac{20}{9}& \text{Uitwerken } \\ & =bx+\frac{20}{9}x-\frac{4}{7}b-\frac{80}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{3}{14})(\frac{-5}{12}-a)& =(\color{red}{a}+\color{orange}{\frac{3}{14}}).(\color{green}{-a}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{3}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{12}a-\frac{3}{14}a-\frac{3}{14}.\frac{5}{12}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{12})+(\frac{-3}{14}))a-\frac{15}{168} & \text{Neem samen} \\ &=-a^2-\frac{53}{84}a-\frac{15}{168} & \text{Maak de som} \\ &=-a^2-\frac{53}{84}a-\frac{5}{56} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{6}-p)(\frac{16}{7}-x)& =(\color{red}{-p}+\color{orange}{\frac{3}{2}}).(\color{green}{-x}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{16}{7}p-\frac{3}{2}x+\frac{3}{2}.\frac{16}{7}& \text{Uitwerken } \\ & =px-\frac{16}{7}p-\frac{3}{2}x+\frac{48}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{16}{7}p-\frac{3}{2}x+\frac{24}{7} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{17}{6})(q+\frac{13}{4})& =(\color{red}{a}+\color{orange}{\frac{-17}{6}}).(\color{green}{q}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{4}a-\frac{17}{6}q-\frac{17}{6}.\frac{13}{4}& \text{Uitwerken } \\ & =aq+\frac{13}{4}a-\frac{17}{6}q-\frac{221}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-4}{13})(b-\frac{3}{8})& =(\color{red}{a}+\color{orange}{\frac{-4}{13}}).(\color{green}{b}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{8}a-\frac{4}{13}b+\frac{4}{13}.\frac{3}{8}& \text{Uitwerken } \\ & =ab-\frac{3}{8}a-\frac{4}{13}b+\frac{12}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{3}{8}a-\frac{4}{13}b+\frac{3}{26} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{10}{15})(\frac{-14}{11}-x)& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{-x}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{14}{11}p+\frac{2}{3}x+\frac{2}{3}.\frac{14}{11}& \text{Uitwerken } \\ & =-px-\frac{14}{11}p+\frac{2}{3}x+\frac{28}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{11}+a)(\frac{-10}{3}-b)& =(\color{red}{a}+\color{orange}{\frac{-3}{11}}).(\color{green}{-b}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{10}{3}a+\frac{3}{11}b+\frac{3}{11}.\frac{10}{3}& \text{Uitwerken } \\ & =-ab-\frac{10}{3}a+\frac{3}{11}b+\frac{30}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{10}{3}a+\frac{3}{11}b+\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-12}{4})(b-\frac{3}{19})& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{19}x-3b+3.\frac{3}{19}& \text{Uitwerken } \\ & =bx-\frac{3}{19}x-3b+\frac{9}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{5}{17}-x)(x+\frac{-20}{4})& =(\color{red}{-x}+\color{orange}{\frac{5}{17}}).(\color{green}{x}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(-5)} + \color{orange}{(\frac{5}{17})} . \color{green}{(x)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -xx+5x+\frac{5}{17}x-\frac{5}{17}.5& \text{Uitwerken } \\ & =-x^2+(5+\frac{5}{17})x-\frac{25}{17} & \text{Neem samen} \\ &=-x^2+\frac{90}{17}x-\frac{25}{17} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{12}{16}-b)(p+\frac{-3}{18})& =(\color{red}{-b}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{6}b+\frac{3}{4}p-\frac{3}{4}.\frac{1}{6}& \text{Uitwerken } \\ & =-bp+\frac{1}{6}b+\frac{3}{4}p-\frac{3}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{6}b+\frac{3}{4}p-\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-11}{15})(p+\frac{4}{2})& =(\color{red}{q}+\color{orange}{\frac{-11}{15}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{-11}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2q-\frac{11}{15}p-\frac{11}{15}.2& \text{Uitwerken } \\ & =pq+2q-\frac{11}{15}p-\frac{22}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-26 21:18:37
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