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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{16}{19})(a+\frac{-13}{10})& =(\color{red}{p}+\color{orange}{\frac{16}{19}}).(\color{green}{a}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{16}{19})} . \color{green}{(a)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{10}p+\frac{16}{19}a-\frac{16}{19}.\frac{13}{10}& \text{Uitwerken } \\ & =ap-\frac{13}{10}p+\frac{16}{19}a-\frac{208}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{13}{10}p+\frac{16}{19}a-\frac{104}{95} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{13}{7}-x)(\frac{10}{6}-a)& =(\color{red}{-x}+\color{orange}{\frac{13}{7}}).(\color{green}{-a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{13}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{3}x-\frac{13}{7}a+\frac{13}{7}.\frac{5}{3}& \text{Uitwerken } \\ & =ax-\frac{5}{3}x-\frac{13}{7}a+\frac{65}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-9}{14}+x)(\frac{12}{19}-p)& =(\color{red}{x}+\color{orange}{\frac{-9}{14}}).(\color{green}{-p}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{12}{19}x+\frac{9}{14}p-\frac{9}{14}.\frac{12}{19}& \text{Uitwerken } \\ & =-px+\frac{12}{19}x+\frac{9}{14}p-\frac{108}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{12}{19}x+\frac{9}{14}p-\frac{54}{133} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-20}{11}-q)(\frac{6}{3}-a)& =(\color{red}{-q}+\color{orange}{\frac{-20}{11}}).(\color{green}{-a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{-20}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq-2q+\frac{20}{11}a-\frac{20}{11}.2& \text{Uitwerken } \\ & =aq-2q+\frac{20}{11}a-\frac{40}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{17}+q)(x+\frac{-14}{16})& =(\color{red}{q}+\color{orange}{\frac{10}{17}}).(\color{green}{x}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{10}{17})} . \color{green}{(x)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{8}q+\frac{10}{17}x-\frac{10}{17}.\frac{7}{8}& \text{Uitwerken } \\ & =qx-\frac{7}{8}q+\frac{10}{17}x-\frac{70}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{7}{8}q+\frac{10}{17}x-\frac{35}{68} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{8}+p)(\frac{-5}{7}+p)& =(\color{red}{p}+\color{orange}{\frac{1}{8}}).(\color{green}{p}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{7}p+\frac{1}{8}p-\frac{1}{8}.\frac{5}{7}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{7})+\frac{1}{8})p-(\frac{-5}{56}) & \text{Neem samen} \\ &=p^2-\frac{33}{56}p-(\frac{-5}{56}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{15}+q)(\frac{18}{17}+q)& =(\color{red}{q}+\color{orange}{\frac{13}{15}}).(\color{green}{q}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{13}{15})} . \color{green}{(q)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{18}{17}q+\frac{13}{15}q+\frac{13}{15}.\frac{18}{17}& \text{Uitwerken } \\ & =q^2+(\frac{18}{17}+\frac{13}{15})q+\frac{234}{255} & \text{Neem samen} \\ &=q^2+\frac{491}{255}q+\frac{234}{255} & \text{Maak de som} \\ &=q^2+\frac{491}{255}q+\frac{78}{85} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-7}{12}-p)(a-\frac{4}{17})& =(\color{red}{-p}+\color{orange}{\frac{-7}{12}}).(\color{green}{a}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{4}{17}p-\frac{7}{12}a+\frac{7}{12}.\frac{4}{17}& \text{Uitwerken } \\ & =-ap+\frac{4}{17}p-\frac{7}{12}a+\frac{28}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{4}{17}p-\frac{7}{12}a+\frac{7}{51} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-15}{11}-x)(\frac{2}{14}+x)& =(\color{red}{-x}+\color{orange}{\frac{-15}{11}}).(\color{green}{x}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{1}{7}x-\frac{15}{11}x-\frac{15}{11}.\frac{1}{7}& \text{Uitwerken } \\ & =-x^2+((\frac{-1}{7})+(\frac{-15}{11}))x-\frac{15}{77} & \text{Neem samen} \\ &=-x^2-\frac{116}{77}x-\frac{15}{77} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-1}{5}-x)(\frac{20}{17}+b)& =(\color{red}{-x}+\color{orange}{\frac{-1}{5}}).(\color{green}{b}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{20}{17}x-\frac{1}{5}b-\frac{1}{5}.\frac{20}{17}& \text{Uitwerken } \\ & =-bx-\frac{20}{17}x-\frac{1}{5}b-\frac{20}{85} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{20}{17}x-\frac{1}{5}b-\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{17}{4}-x)(\frac{2}{20}-p)& =(\color{red}{-x}+\color{orange}{\frac{17}{4}}).(\color{green}{-p}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{17}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{10}x-\frac{17}{4}p+\frac{17}{4}.\frac{1}{10}& \text{Uitwerken } \\ & =px-\frac{1}{10}x-\frac{17}{4}p+\frac{17}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-5}{5}-q)(\frac{-10}{12}+p)& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{6}q-1p+1.\frac{5}{6}& \text{Uitwerken } \\ & =-pq+\frac{5}{6}q-1p+\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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