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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-9}{16})(a-\frac{6}{10})& =(\color{red}{a}+\color{orange}{\frac{-9}{16}}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{5}a-\frac{9}{16}a+\frac{9}{16}.\frac{3}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{5})+(\frac{-9}{16}))a+\frac{27}{80} & \text{Neem samen} \\ &=a^2-\frac{93}{80}a+\frac{27}{80} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-14}{9})(a+\frac{17}{6})& =(\color{red}{x}+\color{orange}{\frac{14}{9}}).(\color{green}{a}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{14}{9})} . \color{green}{(a)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{6}x+\frac{14}{9}a+\frac{14}{9}.\frac{17}{6}& \text{Uitwerken } \\ & =ax+\frac{17}{6}x+\frac{14}{9}a+\frac{238}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{17}{6}x+\frac{14}{9}a+\frac{119}{27} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-5}{4}+p)(b+\frac{7}{4})& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{4}p-\frac{5}{4}b-\frac{5}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =bp+\frac{7}{4}p-\frac{5}{4}b-\frac{35}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{16}{8})(q-\frac{4}{10})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{5}x+2q-2.\frac{2}{5}& \text{Uitwerken } \\ & =qx-\frac{2}{5}x+2q-\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-20}{14}+a)(p-\frac{11}{11})& =(\color{red}{a}+\color{orange}{\frac{-10}{7}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a-\frac{10}{7}p+\frac{10}{7}.1& \text{Uitwerken } \\ & =ap-1a-\frac{10}{7}p+\frac{10}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{5}-a)(a-\frac{11}{2})& =(\color{red}{-a}+\color{orange}{4}).(\color{green}{a}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{11}{2}a+4a-4.\frac{11}{2}& \text{Uitwerken } \\ & =-a^2+(\frac{11}{2}+4)a-\frac{44}{2} & \text{Neem samen} \\ &=-a^2+\frac{19}{2}a-\frac{44}{2} & \text{Maak de som} \\ &=-a^2+\frac{19}{2}a-22 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{-7}{8}-b)(b-\frac{-5}{14})& =(\color{red}{-b}+\color{orange}{\frac{-7}{8}}).(\color{green}{b}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{5}{14}b-\frac{7}{8}b-\frac{7}{8}.\frac{5}{14}& \text{Uitwerken } \\ & =-b^2+((\frac{-5}{14})+(\frac{-7}{8}))b-\frac{35}{112} & \text{Neem samen} \\ &=-b^2-\frac{69}{56}b-\frac{35}{112} & \text{Maak de som} \\ &=-b^2-\frac{69}{56}b-\frac{5}{16} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{12}-a)(\frac{-6}{17}-a)& =(\color{red}{-a}+\color{orange}{\frac{-2}{3}}).(\color{green}{-a}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{6}{17}a+\frac{2}{3}a+\frac{2}{3}.\frac{6}{17}& \text{Uitwerken } \\ & =a^2+(\frac{6}{17}+\frac{2}{3})a+\frac{12}{51} & \text{Neem samen} \\ &=a^2+\frac{52}{51}a+\frac{12}{51} & \text{Maak de som} \\ &=a^2+\frac{52}{51}a+\frac{4}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-18}{11})(p+\frac{6}{5})& =(\color{red}{x}+\color{orange}{\frac{18}{11}}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{18}{11})} . \color{green}{(p)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{6}{5}x+\frac{18}{11}p+\frac{18}{11}.\frac{6}{5}& \text{Uitwerken } \\ & =px+\frac{6}{5}x+\frac{18}{11}p+\frac{108}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-17}{18}-a)(\frac{4}{9}-x)& =(\color{red}{-a}+\color{orange}{\frac{-17}{18}}).(\color{green}{-x}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{9}a+\frac{17}{18}x-\frac{17}{18}.\frac{4}{9}& \text{Uitwerken } \\ & =ax-\frac{4}{9}a+\frac{17}{18}x-\frac{68}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{4}{9}a+\frac{17}{18}x-\frac{34}{81} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{9}{14}+x)(a-\frac{7}{15})& =(\color{red}{x}+\color{orange}{\frac{9}{14}}).(\color{green}{a}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{9}{14})} . \color{green}{(a)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{15}x+\frac{9}{14}a-\frac{9}{14}.\frac{7}{15}& \text{Uitwerken } \\ & =ax-\frac{7}{15}x+\frac{9}{14}a-\frac{63}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{7}{15}x+\frac{9}{14}a-\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-19}{16})(\frac{6}{3}+q)& =(\color{red}{a}+\color{orange}{\frac{19}{16}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{19}{16})} . \color{green}{(q)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2a+\frac{19}{16}q+\frac{19}{16}.2& \text{Uitwerken } \\ & =aq+2a+\frac{19}{16}q+\frac{38}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+2a+\frac{19}{16}q+\frac{19}{8} & \text{Vereenvoudig} \\\end{align}\)
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