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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{17}{2}-b)(\frac{-9}{4}+b)& =(\color{red}{-b}+\color{orange}{\frac{17}{2}}).(\color{green}{b}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{17}{2})} . \color{green}{(b)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{9}{4}b+\frac{17}{2}b-\frac{17}{2}.\frac{9}{4}& \text{Uitwerken } \\ & =-b^2+(\frac{9}{4}+\frac{17}{2})b-\frac{153}{8} & \text{Neem samen} \\ &=-b^2+\frac{43}{4}b-\frac{153}{8} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-6}{6})(\frac{-9}{4}-q)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{4}p-1q-1.\frac{9}{4}& \text{Uitwerken } \\ & =-pq-\frac{9}{4}p-1q-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-15}{11})(\frac{-1}{13}-a)& =(\color{red}{x}+\color{orange}{\frac{-15}{11}}).(\color{green}{-a}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{13}x+\frac{15}{11}a+\frac{15}{11}.\frac{1}{13}& \text{Uitwerken } \\ & =-ax-\frac{1}{13}x+\frac{15}{11}a+\frac{15}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-19}{2})(\frac{-1}{18}-q)& =(\color{red}{q}+\color{orange}{\frac{19}{2}}).(\color{green}{-q}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{19}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{18}q-\frac{19}{2}q-\frac{19}{2}.\frac{1}{18}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{18})+(\frac{-19}{2}))q-\frac{19}{36} & \text{Neem samen} \\ &=-q^2-\frac{172}{18}q-\frac{19}{36} & \text{Maak de som} \\ &=-q^2-\frac{86}{9}q-\frac{19}{36} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-20}{20}+a)(b+\frac{-19}{7})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{7}a-1b+1.\frac{19}{7}& \text{Uitwerken } \\ & =ab-\frac{19}{7}a-1b+\frac{19}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{13}-b)(18-a)& =(\color{red}{-b}+\color{orange}{\frac{-9}{13}}).(\color{green}{-a}+\color{blue}{18})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(18)} + \color{orange}{(\frac{-9}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = ab-18b+\frac{9}{13}a-\frac{9}{13}.18& \text{Uitwerken } \\ & =ab-18b+\frac{9}{13}a-\frac{162}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{17}+b)(\frac{5}{18}+x)& =(\color{red}{b}+\color{orange}{\frac{13}{17}}).(\color{green}{x}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{13}{17})} . \color{green}{(x)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{18}b+\frac{13}{17}x+\frac{13}{17}.\frac{5}{18}& \text{Uitwerken } \\ & =bx+\frac{5}{18}b+\frac{13}{17}x+\frac{65}{306} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-18}{13})(q-(-11))& =(\color{red}{x}+\color{orange}{\frac{-18}{13}}).(\color{green}{q}+\color{blue}{11})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(11)} + \color{orange}{(\frac{-18}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = qx+11x-\frac{18}{13}q-\frac{18}{13}.11& \text{Uitwerken } \\ & =qx+11x-\frac{18}{13}q-\frac{198}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-17}{7})(a+12)& =(\color{red}{a}+\color{orange}{\frac{-17}{7}}).(\color{green}{a}+\color{blue}{12})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(12)} + \color{orange}{(\frac{-17}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = aa+12a-\frac{17}{7}a-\frac{17}{7}.12& \text{Uitwerken } \\ & =a^2+(12+(\frac{-17}{7}))a-(\frac{-204}{7}) & \text{Neem samen} \\ &=a^2+\frac{67}{7}a-(\frac{-204}{7}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-6}{12})(\frac{-16}{19}+b)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{16}{19}b+\frac{1}{2}b-\frac{1}{2}.\frac{16}{19}& \text{Uitwerken } \\ & =b^2+((\frac{-16}{19})+\frac{1}{2})b-(\frac{-16}{38}) & \text{Neem samen} \\ &=b^2-\frac{13}{38}b-(\frac{-16}{38}) & \text{Maak de som} \\ &=b^2-\frac{13}{38}b+\frac{8}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(b-\frac{1}{5})(a-\frac{-11}{8})& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{8}b-\frac{1}{5}a-\frac{1}{5}.\frac{11}{8}& \text{Uitwerken } \\ & =ab+\frac{11}{8}b-\frac{1}{5}a-\frac{11}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-9)(x+\frac{14}{9})& =(\color{red}{p}+\color{orange}{(-9)}).(\color{green}{x}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(-9)} . \color{green}{(x)} + \color{orange}{(-9)} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{14}{9}p-9x-9.\frac{14}{9}& \text{Uitwerken } \\ & =px+\frac{14}{9}p-9x-\frac{126}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{14}{9}p-9x-14 & \text{Vereenvoudig} \\\end{align}\)
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