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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-2}{8})(x+\frac{-4}{12})& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{3}x+\frac{1}{4}x-\frac{1}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{3})+\frac{1}{4})x-(\frac{-1}{12}) & \text{Neem samen} \\ &=x^2-\frac{1}{12}x-(\frac{-1}{12}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(b+(-5))(p+\frac{-12}{6})& =(\color{red}{b}+\color{orange}{(-5)}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(-5)} . \color{green}{(p)} + \color{orange}{(-5)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bp-2b-5p+5.2& \text{Uitwerken } \\ & =bp-2b-5p+10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-1}{11})(\frac{18}{15}-b)& =(\color{red}{x}+\color{orange}{\frac{-1}{11}}).(\color{green}{-b}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{6}{5}x+\frac{1}{11}b-\frac{1}{11}.\frac{6}{5}& \text{Uitwerken } \\ & =-bx+\frac{6}{5}x+\frac{1}{11}b-\frac{6}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{18}{4}-a)(\frac{-9}{13}+a)& =(\color{red}{-a}+\color{orange}{\frac{9}{2}}).(\color{green}{a}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{9}{2})} . \color{green}{(a)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{9}{13}a+\frac{9}{2}a-\frac{9}{2}.\frac{9}{13}& \text{Uitwerken } \\ & =-a^2+(\frac{9}{13}+\frac{9}{2})a-\frac{81}{26} & \text{Neem samen} \\ &=-a^2+\frac{135}{26}a-\frac{81}{26} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(p-\frac{5}{6})(p+\frac{1}{15})& =(\color{red}{p}+\color{orange}{\frac{-5}{6}}).(\color{green}{p}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{15}p-\frac{5}{6}p-\frac{5}{6}.\frac{1}{15}& \text{Uitwerken } \\ & =p^2+(\frac{1}{15}+(\frac{-5}{6}))p-(\frac{-5}{90}) & \text{Neem samen} \\ &=p^2-\frac{23}{30}p-(\frac{-5}{90}) & \text{Maak de som} \\ &=p^2-\frac{23}{30}p+\frac{1}{18} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-13}{4})(a-\frac{-1}{6})& =(\color{red}{x}+\color{orange}{\frac{-13}{4}}).(\color{green}{a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{6}x-\frac{13}{4}a-\frac{13}{4}.\frac{1}{6}& \text{Uitwerken } \\ & =ax+\frac{1}{6}x-\frac{13}{4}a-\frac{13}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{13}{18})(p+\frac{14}{7})& =(\color{red}{q}+\color{orange}{\frac{-13}{18}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{-13}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2q-\frac{13}{18}p-\frac{13}{18}.2& \text{Uitwerken } \\ & =pq+2q-\frac{13}{18}p-\frac{26}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+2q-\frac{13}{18}p-\frac{13}{9} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{5}+x)(\frac{-18}{18}-a)& =(\color{red}{x}+\color{orange}{\frac{12}{5}}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{12}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ax-1x-\frac{12}{5}a-\frac{12}{5}.1& \text{Uitwerken } \\ & =-ax-1x-\frac{12}{5}a-\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{20}{8}+q)(\frac{9}{13}-b)& =(\color{red}{q}+\color{orange}{\frac{5}{2}}).(\color{green}{-b}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{9}{13}q-\frac{5}{2}b+\frac{5}{2}.\frac{9}{13}& \text{Uitwerken } \\ & =-bq+\frac{9}{13}q-\frac{5}{2}b+\frac{45}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-20}{19}+a)(12-x)& =(\color{red}{a}+\color{orange}{\frac{-20}{19}}).(\color{green}{-x}+\color{blue}{12})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(12)} + \color{orange}{(\frac{-20}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = -ax+12a+\frac{20}{19}x-\frac{20}{19}.12& \text{Uitwerken } \\ & =-ax+12a+\frac{20}{19}x-\frac{240}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{17}{15})(\frac{-6}{8}+p)& =(\color{red}{p}+\color{orange}{\frac{17}{15}}).(\color{green}{p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{17}{15})} . \color{green}{(p)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{4}p+\frac{17}{15}p-\frac{17}{15}.\frac{3}{4}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{4})+\frac{17}{15})p-(\frac{-51}{60}) & \text{Neem samen} \\ &=p^2+\frac{23}{60}p-(\frac{-51}{60}) & \text{Maak de som} \\ &=p^2+\frac{23}{60}p+\frac{17}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{11}{3}+b)(x+\frac{-6}{20})& =(\color{red}{b}+\color{orange}{\frac{11}{3}}).(\color{green}{x}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{11}{3})} . \color{green}{(x)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{10}b+\frac{11}{3}x-\frac{11}{3}.\frac{3}{10}& \text{Uitwerken } \\ & =bx-\frac{3}{10}b+\frac{11}{3}x-\frac{33}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{3}{10}b+\frac{11}{3}x-\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
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