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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-1}{16}-a)(a+\frac{-18}{11})& =(\color{red}{-a}+\color{orange}{\frac{-1}{16}}).(\color{green}{a}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{18}{11}a-\frac{1}{16}a+\frac{1}{16}.\frac{18}{11}& \text{Uitwerken } \\ & =-a^2+(\frac{18}{11}+(\frac{-1}{16}))a+(\frac{-18}{176}) & \text{Neem samen} \\ &=-a^2+\frac{277}{176}a+(\frac{-18}{176}) & \text{Maak de som} \\ &=-a^2+\frac{277}{176}a+(\frac{-9}{88}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{11}+a)(\frac{8}{12}+x)& =(\color{red}{a}+\color{orange}{\frac{-17}{11}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-17}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}a-\frac{17}{11}x-\frac{17}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}a-\frac{17}{11}x-\frac{34}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-5}{11})(p-\frac{-17}{17})& =(\color{red}{a}+\color{orange}{\frac{5}{11}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{11})} . \color{green}{(p)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1a+\frac{5}{11}p+\frac{5}{11}.1& \text{Uitwerken } \\ & =ap+1a+\frac{5}{11}p+\frac{5}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{18}{18})(q-\frac{-6}{16})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{8}x-1q-1.\frac{3}{8}& \text{Uitwerken } \\ & =qx+\frac{3}{8}x-1q-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-7}{17})(x+\frac{-5}{19})& =(\color{red}{b}+\color{orange}{\frac{7}{17}}).(\color{green}{x}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{7}{17})} . \color{green}{(x)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{19}b+\frac{7}{17}x-\frac{7}{17}.\frac{5}{19}& \text{Uitwerken } \\ & =bx-\frac{5}{19}b+\frac{7}{17}x-\frac{35}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-6}{11})(x-\frac{9}{5})& =(\color{red}{q}+\color{orange}{\frac{-6}{11}}).(\color{green}{x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{5}q-\frac{6}{11}x+\frac{6}{11}.\frac{9}{5}& \text{Uitwerken } \\ & =qx-\frac{9}{5}q-\frac{6}{11}x+\frac{54}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{6}{14})(\frac{6}{20}+p)& =(\color{red}{q}+\color{orange}{\frac{-3}{7}}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{10}q-\frac{3}{7}p-\frac{3}{7}.\frac{3}{10}& \text{Uitwerken } \\ & =pq+\frac{3}{10}q-\frac{3}{7}p-\frac{9}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-10}{8})(\frac{12}{7}+a)& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{a}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{12}{7}a-\frac{5}{4}a-\frac{5}{4}.\frac{12}{7}& \text{Uitwerken } \\ & =a^2+(\frac{12}{7}+(\frac{-5}{4}))a-(\frac{-60}{28}) & \text{Neem samen} \\ &=a^2+\frac{13}{28}a-(\frac{-60}{28}) & \text{Maak de som} \\ &=a^2+\frac{13}{28}a+\frac{15}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(b+\frac{20}{8})(b+\frac{14}{7})& =(\color{red}{b}+\color{orange}{\frac{5}{2}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bb+2b+\frac{5}{2}b+\frac{5}{2}.2& \text{Uitwerken } \\ & =b^2+(2+\frac{5}{2})b+\frac{10}{2} & \text{Neem samen} \\ &=b^2+\frac{9}{2}b+\frac{10}{2} & \text{Maak de som} \\ &=b^2+\frac{9}{2}b+5 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-19}{11}+b)(\frac{-1}{15}-x)& =(\color{red}{b}+\color{orange}{\frac{-19}{11}}).(\color{green}{-x}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{15}b+\frac{19}{11}x+\frac{19}{11}.\frac{1}{15}& \text{Uitwerken } \\ & =-bx-\frac{1}{15}b+\frac{19}{11}x+\frac{19}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-8}{13})(p-\frac{-17}{8})& =(\color{red}{x}+\color{orange}{\frac{8}{13}}).(\color{green}{p}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{8}{13})} . \color{green}{(p)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{8}x+\frac{8}{13}p+\frac{8}{13}.\frac{17}{8}& \text{Uitwerken } \\ & =px+\frac{17}{8}x+\frac{8}{13}p+\frac{136}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{17}{8}x+\frac{8}{13}p+\frac{17}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-8}{2})(\frac{18}{19}-b)& =(\color{red}{b}+\color{orange}{4}).(\color{green}{-b}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(4)} . \color{green}{(-b)} + \color{orange}{(4)} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{18}{19}b-4b+4.\frac{18}{19}& \text{Uitwerken } \\ & =-b^2+(\frac{18}{19}+(-4))b+(\frac{-72}{19}) & \text{Neem samen} \\ &=-b^2-\frac{58}{19}b+(\frac{-72}{19}) & \text{Maak de som} \\\end{align}\)
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