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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{8}{10})(\frac{-15}{7}+b)& =(\color{red}{a}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{7}a+\frac{4}{5}b-\frac{4}{5}.\frac{15}{7}& \text{Uitwerken } \\ & =ab-\frac{15}{7}a+\frac{4}{5}b-\frac{60}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{15}{7}a+\frac{4}{5}b-\frac{12}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-16}{11}-x)(x+\frac{-18}{6})& =(\color{red}{-x}+\color{orange}{\frac{-16}{11}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-16}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -xx+3x-\frac{16}{11}x+\frac{16}{11}.3& \text{Uitwerken } \\ & =-x^2+(3+(\frac{-16}{11}))x+(\frac{-48}{11}) & \text{Neem samen} \\ &=-x^2+\frac{17}{11}x+(\frac{-48}{11}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{16}-a)(\frac{5}{3}-x)& =(\color{red}{-a}+\color{orange}{\frac{1}{16}}).(\color{green}{-x}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{1}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{3}a-\frac{1}{16}x+\frac{1}{16}.\frac{5}{3}& \text{Uitwerken } \\ & =ax-\frac{5}{3}a-\frac{1}{16}x+\frac{5}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-14}{2})(a+\frac{-19}{11})& =(\color{red}{a}+\color{orange}{(-7)}).(\color{green}{a}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(-7)} . \color{green}{(a)} + \color{orange}{(-7)} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{19}{11}a-7a+7.\frac{19}{11}& \text{Uitwerken } \\ & =a^2+((\frac{-19}{11})+(-7))a+\frac{133}{11} & \text{Neem samen} \\ &=a^2-\frac{96}{11}a+\frac{133}{11} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{5}-x)(\frac{9}{14}-a)& =(\color{red}{-x}+\color{orange}{\frac{16}{5}}).(\color{green}{-a}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{16}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{14}x-\frac{16}{5}a+\frac{16}{5}.\frac{9}{14}& \text{Uitwerken } \\ & =ax-\frac{9}{14}x-\frac{16}{5}a+\frac{144}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{9}{14}x-\frac{16}{5}a+\frac{72}{35} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{2}{6}+p)(b-\frac{14}{13})& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{14}{13}p+\frac{1}{3}b-\frac{1}{3}.\frac{14}{13}& \text{Uitwerken } \\ & =bp-\frac{14}{13}p+\frac{1}{3}b-\frac{14}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{17}+x)(\frac{-5}{9}+b)& =(\color{red}{x}+\color{orange}{\frac{11}{17}}).(\color{green}{b}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{11}{17})} . \color{green}{(b)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{9}x+\frac{11}{17}b-\frac{11}{17}.\frac{5}{9}& \text{Uitwerken } \\ & =bx-\frac{5}{9}x+\frac{11}{17}b-\frac{55}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{3}{17}+p)(b-\frac{20}{11})& =(\color{red}{p}+\color{orange}{\frac{3}{17}}).(\color{green}{b}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{3}{17})} . \color{green}{(b)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{20}{11}p+\frac{3}{17}b-\frac{3}{17}.\frac{20}{11}& \text{Uitwerken } \\ & =bp-\frac{20}{11}p+\frac{3}{17}b-\frac{60}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{6}{19})(b-\frac{-14}{17})& =(\color{red}{a}+\color{orange}{\frac{6}{19}}).(\color{green}{b}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{6}{19})} . \color{green}{(b)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{14}{17}a+\frac{6}{19}b+\frac{6}{19}.\frac{14}{17}& \text{Uitwerken } \\ & =ab+\frac{14}{17}a+\frac{6}{19}b+\frac{84}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{1}{14})(15+q)& =(\color{red}{x}+\color{orange}{\frac{1}{14}}).(\color{green}{q}+\color{blue}{15})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(15)} + \color{orange}{(\frac{1}{14})} . \color{green}{(q)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(15)}& \text{Boogjes en uitschrijven} \\ & = qx+15x+\frac{1}{14}q+\frac{1}{14}.15& \text{Uitwerken } \\ & =qx+15x+\frac{1}{14}q+\frac{15}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{9}{20}-q)(\frac{4}{2}+b)& =(\color{red}{-q}+\color{orange}{\frac{9}{20}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{9}{20})} . \color{green}{(b)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bq-2q+\frac{9}{20}b+\frac{9}{20}.2& \text{Uitwerken } \\ & =-bq-2q+\frac{9}{20}b+\frac{18}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-2q+\frac{9}{20}b+\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p-\frac{9}{8})(b-\frac{-12}{16})& =(\color{red}{p}+\color{orange}{\frac{-9}{8}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{4}p-\frac{9}{8}b-\frac{9}{8}.\frac{3}{4}& \text{Uitwerken } \\ & =bp+\frac{3}{4}p-\frac{9}{8}b-\frac{27}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-09 01:09:49
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