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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{12}{18})(q-\frac{-6}{16})& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{8}a+\frac{2}{3}q+\frac{2}{3}.\frac{3}{8}& \text{Uitwerken } \\ & =aq+\frac{3}{8}a+\frac{2}{3}q+\frac{6}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{8}a+\frac{2}{3}q+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{2}+x)(\frac{-1}{19}+x)& =(\color{red}{x}+\color{orange}{\frac{19}{2}}).(\color{green}{x}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{19}{2})} . \color{green}{(x)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{19}x+\frac{19}{2}x-\frac{19}{2}.\frac{1}{19}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{19})+\frac{19}{2})x-(\frac{-19}{38}) & \text{Neem samen} \\ &=x^2+\frac{359}{38}x-(\frac{-19}{38}) & \text{Maak de som} \\ &=x^2+\frac{359}{38}x+\frac{1}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(b+\frac{5}{17})(p+\frac{-5}{10})& =(\color{red}{b}+\color{orange}{\frac{5}{17}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{5}{17})} . \color{green}{(p)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{2}b+\frac{5}{17}p-\frac{5}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =bp-\frac{1}{2}b+\frac{5}{17}p-\frac{5}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{9}{19})((-12)-x)& =(\color{red}{q}+\color{orange}{\frac{9}{19}}).(\color{green}{-x}+\color{blue}{(-12)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(-12)} + \color{orange}{(\frac{9}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = -qx-12q-\frac{9}{19}x-\frac{9}{19}.12& \text{Uitwerken } \\ & =-qx-12q-\frac{9}{19}x-\frac{108}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{5}-a)(x+\frac{-3}{8})& =(\color{red}{-a}+\color{orange}{\frac{14}{5}}).(\color{green}{x}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{14}{5})} . \color{green}{(x)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{8}a+\frac{14}{5}x-\frac{14}{5}.\frac{3}{8}& \text{Uitwerken } \\ & =-ax+\frac{3}{8}a+\frac{14}{5}x-\frac{42}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{3}{8}a+\frac{14}{5}x-\frac{21}{20} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{5}-p)(\frac{-18}{15}-a)& =(\color{red}{-p}+\color{orange}{\frac{-14}{5}}).(\color{green}{-a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{6}{5}p+\frac{14}{5}a+\frac{14}{5}.\frac{6}{5}& \text{Uitwerken } \\ & =ap+\frac{6}{5}p+\frac{14}{5}a+\frac{84}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{12}{3}-p)(\frac{-3}{8}-a)& =(\color{red}{-p}+\color{orange}{4}).(\color{green}{-a}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(4)} . \color{green}{(-a)} + \color{orange}{(4)} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{8}p-4a-4.\frac{3}{8}& \text{Uitwerken } \\ & =ap+\frac{3}{8}p-4a-\frac{12}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{8}p-4a-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-12}{6})(\frac{17}{2}-p)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-p}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(2)} . \color{green}{(-p)} + \color{orange}{(2)} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{17}{2}p-2p+2.\frac{17}{2}& \text{Uitwerken } \\ & =-p^2+(\frac{17}{2}+(-2))p+(\frac{-34}{2}) & \text{Neem samen} \\ &=-p^2+\frac{13}{2}p+(\frac{-34}{2}) & \text{Maak de som} \\ &=-p^2+\frac{13}{2}p+(-17) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-16}{18}+a)(\frac{17}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{-8}{9}}).(\color{green}{p}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{4}a-\frac{8}{9}p-\frac{8}{9}.\frac{17}{4}& \text{Uitwerken } \\ & =ap+\frac{17}{4}a-\frac{8}{9}p-\frac{136}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{17}{4}a-\frac{8}{9}p-\frac{34}{9} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-7}{5})(p+\frac{1}{7})& =(\color{red}{q}+\color{orange}{\frac{7}{5}}).(\color{green}{p}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{7}q+\frac{7}{5}p+\frac{7}{5}.\frac{1}{7}& \text{Uitwerken } \\ & =pq+\frac{1}{7}q+\frac{7}{5}p+\frac{7}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{7}q+\frac{7}{5}p+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{11}-x)(b-\frac{15}{5})& =(\color{red}{-x}+\color{orange}{\frac{-19}{11}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-19}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bx+3x-\frac{19}{11}b+\frac{19}{11}.3& \text{Uitwerken } \\ & =-bx+3x-\frac{19}{11}b+\frac{57}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-12}{17}-q)(p+\frac{14}{5})& =(\color{red}{-q}+\color{orange}{\frac{-12}{17}}).(\color{green}{p}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{14}{5}q-\frac{12}{17}p-\frac{12}{17}.\frac{14}{5}& \text{Uitwerken } \\ & =-pq-\frac{14}{5}q-\frac{12}{17}p-\frac{168}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-24 03:04:55
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