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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{8}{12}+q)(\frac{-16}{16}-x)& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{2}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx-1q-\frac{2}{3}x-\frac{2}{3}.1& \text{Uitwerken } \\ & =-qx-1q-\frac{2}{3}x-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{19}+q)(\frac{-13}{14}-b)& =(\color{red}{q}+\color{orange}{\frac{7}{19}}).(\color{green}{-b}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{7}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{14}q-\frac{7}{19}b-\frac{7}{19}.\frac{13}{14}& \text{Uitwerken } \\ & =-bq-\frac{13}{14}q-\frac{7}{19}b-\frac{91}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{13}{14}q-\frac{7}{19}b-\frac{13}{38} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-2}{19}-q)(q+\frac{11}{15})& =(\color{red}{-q}+\color{orange}{\frac{-2}{19}}).(\color{green}{q}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{11}{15}q-\frac{2}{19}q-\frac{2}{19}.\frac{11}{15}& \text{Uitwerken } \\ & =-q^2+((\frac{-11}{15})+(\frac{-2}{19}))q-\frac{22}{285} & \text{Neem samen} \\ &=-q^2-\frac{239}{285}q-\frac{22}{285} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b+\frac{10}{14})(\frac{11}{2}-q)& =(\color{red}{b}+\color{orange}{\frac{5}{7}}).(\color{green}{-q}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{5}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{11}{2}b-\frac{5}{7}q+\frac{5}{7}.\frac{11}{2}& \text{Uitwerken } \\ & =-bq+\frac{11}{2}b-\frac{5}{7}q+\frac{55}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{12}+p)(p-\frac{5}{15})& =(\color{red}{p}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{3}p-\frac{4}{3}p+\frac{4}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{3})+(\frac{-4}{3}))p+\frac{4}{9} & \text{Neem samen} \\ &=p^2-\frac{5}{3}p+\frac{4}{9} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-15}{4})(\frac{-7}{3}+b)& =(\color{red}{q}+\color{orange}{\frac{-15}{4}}).(\color{green}{b}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{3}q-\frac{15}{4}b+\frac{15}{4}.\frac{7}{3}& \text{Uitwerken } \\ & =bq-\frac{7}{3}q-\frac{15}{4}b+\frac{105}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{7}{3}q-\frac{15}{4}b+\frac{35}{4} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{3}{17}+a)(\frac{-15}{6}-p)& =(\color{red}{a}+\color{orange}{\frac{3}{17}}).(\color{green}{-p}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{3}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{2}a-\frac{3}{17}p-\frac{3}{17}.\frac{5}{2}& \text{Uitwerken } \\ & =-ap-\frac{5}{2}a-\frac{3}{17}p-\frac{15}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{17}{13})(\frac{6}{3}-q)& =(\color{red}{b}+\color{orange}{\frac{17}{13}}).(\color{green}{-q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{17}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bq+2b-\frac{17}{13}q+\frac{17}{13}.2& \text{Uitwerken } \\ & =-bq+2b-\frac{17}{13}q+\frac{34}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-6}{2})(\frac{17}{9}+p)& =(\color{red}{b}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{17}{9}b+3p+3.\frac{17}{9}& \text{Uitwerken } \\ & =bp+\frac{17}{9}b+3p+\frac{51}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{17}{9}b+3p+\frac{17}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-20}{6})(a-\frac{-9}{13})& =(\color{red}{a}+\color{orange}{\frac{-10}{3}}).(\color{green}{a}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{9}{13}a-\frac{10}{3}a-\frac{10}{3}.\frac{9}{13}& \text{Uitwerken } \\ & =a^2+(\frac{9}{13}+(\frac{-10}{3}))a-(\frac{-90}{39}) & \text{Neem samen} \\ &=a^2-\frac{103}{39}a-(\frac{-90}{39}) & \text{Maak de som} \\ &=a^2-\frac{103}{39}a+\frac{30}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(a+\frac{2}{18})(\frac{-12}{18}+q)& =(\color{red}{a}+\color{orange}{\frac{1}{9}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{3}a+\frac{1}{9}q-\frac{1}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =aq-\frac{2}{3}a+\frac{1}{9}q-\frac{2}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{4}{14}+q)((-16)+q)& =(\color{red}{q}+\color{orange}{\frac{2}{7}}).(\color{green}{q}+\color{blue}{(-16)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-16)} + \color{orange}{(\frac{2}{7})} . \color{green}{(q)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = qq-16q+\frac{2}{7}q-\frac{2}{7}.16& \text{Uitwerken } \\ & =q^2+((-16)+\frac{2}{7})q-(\frac{-32}{7}) & \text{Neem samen} \\ &=q^2-\frac{110}{7}q-(\frac{-32}{7}) & \text{Maak de som} \\\end{align}\)
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