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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{3}{5})(a+\frac{-15}{11})& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{11}q-\frac{3}{5}a+\frac{3}{5}.\frac{15}{11}& \text{Uitwerken } \\ & =aq-\frac{15}{11}q-\frac{3}{5}a+\frac{45}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{15}{11}q-\frac{3}{5}a+\frac{9}{11} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b-\frac{15}{10})(x+\frac{-13}{19})& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{x}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{19}b-\frac{3}{2}x+\frac{3}{2}.\frac{13}{19}& \text{Uitwerken } \\ & =bx-\frac{13}{19}b-\frac{3}{2}x+\frac{39}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{1}{17})(\frac{6}{15}-a)& =(\color{red}{a}+\color{orange}{\frac{1}{17}}).(\color{green}{-a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{1}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{2}{5}a-\frac{1}{17}a+\frac{1}{17}.\frac{2}{5}& \text{Uitwerken } \\ & =-a^2+(\frac{2}{5}+(\frac{-1}{17}))a+(\frac{-2}{85}) & \text{Neem samen} \\ &=-a^2+\frac{29}{85}a+(\frac{-2}{85}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-7}{13})(\frac{-12}{12}-p)& =(\color{red}{b}+\color{orange}{\frac{-7}{13}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-7}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1b+\frac{7}{13}p+\frac{7}{13}.1& \text{Uitwerken } \\ & =-bp-1b+\frac{7}{13}p+\frac{7}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{8}{7}-p)(\frac{-20}{19}-b)& =(\color{red}{-p}+\color{orange}{\frac{8}{7}}).(\color{green}{-b}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{8}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{20}{19}p-\frac{8}{7}b-\frac{8}{7}.\frac{20}{19}& \text{Uitwerken } \\ & =bp+\frac{20}{19}p-\frac{8}{7}b-\frac{160}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-8}{12})(\frac{-18}{10}+b)& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{5}p-\frac{2}{3}b+\frac{2}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =bp-\frac{9}{5}p-\frac{2}{3}b+\frac{18}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{9}{5}p-\frac{2}{3}b+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{9}-x)(\frac{-14}{20}-b)& =(\color{red}{-x}+\color{orange}{\frac{11}{9}}).(\color{green}{-b}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{11}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{10}x-\frac{11}{9}b-\frac{11}{9}.\frac{7}{10}& \text{Uitwerken } \\ & =bx+\frac{7}{10}x-\frac{11}{9}b-\frac{77}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{20}{19}-x)(x-\frac{-12}{12})& =(\color{red}{-x}+\color{orange}{\frac{20}{19}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{20}{19})} . \color{green}{(x)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -xx-1x+\frac{20}{19}x+\frac{20}{19}.1& \text{Uitwerken } \\ & =-x^2+((-1)+\frac{20}{19})x+(\frac{-20}{19}) & \text{Neem samen} \\ &=-x^2+\frac{1}{19}x+(\frac{-20}{19}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(q-(-20))(\frac{-14}{14}+x)& =(\color{red}{q}+\color{orange}{20}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(20)} . \color{green}{(x)} + \color{orange}{(20)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q+20x-20.1& \text{Uitwerken } \\ & =qx-1q+20x-20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-19}{14}+b)(a-\frac{-13}{13})& =(\color{red}{b}+\color{orange}{\frac{-19}{14}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1b-\frac{19}{14}a-\frac{19}{14}.1& \text{Uitwerken } \\ & =ab+1b-\frac{19}{14}a-\frac{19}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-4}{2})(x+\frac{17}{11})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{11}q-2x-2.\frac{17}{11}& \text{Uitwerken } \\ & =qx+\frac{17}{11}q-2x-\frac{34}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{3}-a)(p+\frac{-8}{16})& =(\color{red}{-a}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{2}a+3p-3.\frac{1}{2}& \text{Uitwerken } \\ & =-ap+\frac{1}{2}a+3p-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-01 05:28:27
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