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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-14}{2}+x)(a+\frac{15}{14})& =(\color{red}{x}+\color{orange}{(-7)}).(\color{green}{a}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(-7)} . \color{green}{(a)} + \color{orange}{(-7)} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{15}{14}x-7a-7.\frac{15}{14}& \text{Uitwerken } \\ & =ax+\frac{15}{14}x-7a-\frac{105}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{15}{14}x-7a-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q-\frac{2}{14})(p+\frac{11}{15})& =(\color{red}{q}+\color{orange}{\frac{-1}{7}}).(\color{green}{p}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{15}q-\frac{1}{7}p-\frac{1}{7}.\frac{11}{15}& \text{Uitwerken } \\ & =pq+\frac{11}{15}q-\frac{1}{7}p-\frac{11}{105} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{5}{11})(\frac{-16}{9}-q)& =(\color{red}{q}+\color{orange}{\frac{-5}{11}}).(\color{green}{-q}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{16}{9}q+\frac{5}{11}q+\frac{5}{11}.\frac{16}{9}& \text{Uitwerken } \\ & =-q^2+((\frac{-16}{9})+\frac{5}{11})q+(\frac{-80}{99}) & \text{Neem samen} \\ &=-q^2-\frac{131}{99}q+(\frac{-80}{99}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-16}{12}-a)(\frac{13}{4}-a)& =(\color{red}{-a}+\color{orange}{\frac{-4}{3}}).(\color{green}{-a}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{13}{4}a+\frac{4}{3}a-\frac{4}{3}.\frac{13}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-13}{4})+\frac{4}{3})a-(\frac{-52}{12}) & \text{Neem samen} \\ &=a^2-\frac{23}{12}a-(\frac{-52}{12}) & \text{Maak de som} \\ &=a^2-\frac{23}{12}a+\frac{13}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(x-\frac{14}{15})(\frac{8}{10}+x)& =(\color{red}{x}+\color{orange}{\frac{-14}{15}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{4}{5}x-\frac{14}{15}x-\frac{14}{15}.\frac{4}{5}& \text{Uitwerken } \\ & =x^2+(\frac{4}{5}+(\frac{-14}{15}))x-(\frac{-56}{75}) & \text{Neem samen} \\ &=x^2-\frac{2}{15}x-(\frac{-56}{75}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(p-\frac{7}{5})(a-\frac{-10}{2})& =(\color{red}{p}+\color{orange}{\frac{-7}{5}}).(\color{green}{a}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(5)} + \color{orange}{(\frac{-7}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ap+5p-\frac{7}{5}a-\frac{7}{5}.5& \text{Uitwerken } \\ & =ap+5p-\frac{7}{5}a-\frac{35}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+5p-\frac{7}{5}a-7 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{8}{14})(\frac{-12}{12}+a)& =(\color{red}{x}+\color{orange}{\frac{-4}{7}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x-\frac{4}{7}a+\frac{4}{7}.1& \text{Uitwerken } \\ & =ax-1x-\frac{4}{7}a+\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{6}{20})(b+\frac{-2}{15})& =(\color{red}{q}+\color{orange}{\frac{3}{10}}).(\color{green}{b}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(\frac{3}{10})} . \color{green}{(b)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{15}q+\frac{3}{10}b-\frac{3}{10}.\frac{2}{15}& \text{Uitwerken } \\ & =bq-\frac{2}{15}q+\frac{3}{10}b-\frac{6}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{2}{15}q+\frac{3}{10}b-\frac{1}{25} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{11}{8})(\frac{-2}{10}+p)& =(\color{red}{p}+\color{orange}{\frac{11}{8}}).(\color{green}{p}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{11}{8})} . \color{green}{(p)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{5}p+\frac{11}{8}p-\frac{11}{8}.\frac{1}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{5})+\frac{11}{8})p-(\frac{-11}{40}) & \text{Neem samen} \\ &=p^2+\frac{47}{40}p-(\frac{-11}{40}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{12}{12}-b)(\frac{-15}{14}-q)& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{14}b-1q-1.\frac{15}{14}& \text{Uitwerken } \\ & =bq+\frac{15}{14}b-1q-\frac{15}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-13}{13})(q-\frac{-6}{9})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{3}b+1q+1.\frac{2}{3}& \text{Uitwerken } \\ & =bq+\frac{2}{3}b+1q+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{15}-b)(x+\frac{6}{2})& =(\color{red}{-b}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(3)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -bx-3b-\frac{2}{3}x-\frac{2}{3}.3& \text{Uitwerken } \\ & =-bx-3b-\frac{2}{3}x-\frac{6}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-3b-\frac{2}{3}x-2 & \text{Vereenvoudig} \\\end{align}\)
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