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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{-3}{6})(\frac{-5}{10}-b)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{2}x+\frac{1}{2}b+\frac{1}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =-bx-\frac{1}{2}x+\frac{1}{2}b+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-14}{20})(\frac{-4}{11}+p)& =(\color{red}{a}+\color{orange}{\frac{-7}{10}}).(\color{green}{p}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{4}{11}a-\frac{7}{10}p+\frac{7}{10}.\frac{4}{11}& \text{Uitwerken } \\ & =ap-\frac{4}{11}a-\frac{7}{10}p+\frac{28}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{4}{11}a-\frac{7}{10}p+\frac{14}{55} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-4}{2}+b)(x-\frac{-19}{7})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{7}b-2x-2.\frac{19}{7}& \text{Uitwerken } \\ & =bx+\frac{19}{7}b-2x-\frac{38}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{18}{19})(\frac{12}{9}-a)& =(\color{red}{b}+\color{orange}{\frac{-18}{19}}).(\color{green}{-a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{4}{3}b+\frac{18}{19}a-\frac{18}{19}.\frac{4}{3}& \text{Uitwerken } \\ & =-ab+\frac{4}{3}b+\frac{18}{19}a-\frac{72}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{4}{3}b+\frac{18}{19}a-\frac{24}{19} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-15}{9})(b+\frac{-9}{3})& =(\color{red}{a}+\color{orange}{\frac{-5}{3}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ab-3a-\frac{5}{3}b+\frac{5}{3}.3& \text{Uitwerken } \\ & =ab-3a-\frac{5}{3}b+\frac{15}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-3a-\frac{5}{3}b+5 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{6}{4})(x+\frac{8}{13})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{x}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{8}{13}q-\frac{3}{2}x-\frac{3}{2}.\frac{8}{13}& \text{Uitwerken } \\ & =qx+\frac{8}{13}q-\frac{3}{2}x-\frac{24}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{8}{13}q-\frac{3}{2}x-\frac{12}{13} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-6}{8}-p)(q+\frac{2}{19})& =(\color{red}{-p}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{19}p-\frac{3}{4}q-\frac{3}{4}.\frac{2}{19}& \text{Uitwerken } \\ & =-pq-\frac{2}{19}p-\frac{3}{4}q-\frac{6}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{2}{19}p-\frac{3}{4}q-\frac{3}{38} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-9}{8}-b)(\frac{-10}{15}-p)& =(\color{red}{-b}+\color{orange}{\frac{-9}{8}}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{3}b+\frac{9}{8}p+\frac{9}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =bp+\frac{2}{3}b+\frac{9}{8}p+\frac{18}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{3}b+\frac{9}{8}p+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{3}{10}+b)(a-\frac{2}{13})& =(\color{red}{b}+\color{orange}{\frac{3}{10}}).(\color{green}{a}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{13}b+\frac{3}{10}a-\frac{3}{10}.\frac{2}{13}& \text{Uitwerken } \\ & =ab-\frac{2}{13}b+\frac{3}{10}a-\frac{6}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{2}{13}b+\frac{3}{10}a-\frac{3}{65} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-4}{13})(b-\frac{10}{16})& =(\color{red}{a}+\color{orange}{\frac{-4}{13}}).(\color{green}{b}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{8}a-\frac{4}{13}b+\frac{4}{13}.\frac{5}{8}& \text{Uitwerken } \\ & =ab-\frac{5}{8}a-\frac{4}{13}b+\frac{20}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{8}a-\frac{4}{13}b+\frac{5}{26} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-2}{14})(\frac{12}{12}-b)& =(\color{red}{x}+\color{orange}{\frac{1}{7}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1x-\frac{1}{7}b+\frac{1}{7}.1& \text{Uitwerken } \\ & =-bx+1x-\frac{1}{7}b+\frac{1}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+(-15))(\frac{-2}{6}-x)& =(\color{red}{x}+\color{orange}{(-15)}).(\color{green}{-x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(-15)} . \color{green}{(-x)} + \color{orange}{(-15)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{1}{3}x+15x+15.\frac{1}{3}& \text{Uitwerken } \\ & =-x^2+((\frac{-1}{3})+15)x+(\frac{-15}{3}) & \text{Neem samen} \\ &=-x^2+\frac{44}{3}x+(\frac{-15}{3}) & \text{Maak de som} \\ &=-x^2+\frac{44}{3}x+(-5) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-17 17:07:34
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