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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{20}-a)(b-\frac{1}{17})& =(\color{red}{-a}+\color{orange}{\frac{3}{20}}).(\color{green}{b}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{3}{20})} . \color{green}{(b)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{17}a+\frac{3}{20}b-\frac{3}{20}.\frac{1}{17}& \text{Uitwerken } \\ & =-ab+\frac{1}{17}a+\frac{3}{20}b-\frac{3}{340} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{15}-a)(q+\frac{15}{9})& =(\color{red}{-a}+\color{orange}{\frac{-17}{15}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{3}a-\frac{17}{15}q-\frac{17}{15}.\frac{5}{3}& \text{Uitwerken } \\ & =-aq-\frac{5}{3}a-\frac{17}{15}q-\frac{85}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{5}{3}a-\frac{17}{15}q-\frac{17}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{19}{20})(p+\frac{13}{10})& =(\color{red}{x}+\color{orange}{\frac{-19}{20}}).(\color{green}{p}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{10}x-\frac{19}{20}p-\frac{19}{20}.\frac{13}{10}& \text{Uitwerken } \\ & =px+\frac{13}{10}x-\frac{19}{20}p-\frac{247}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{3}{20}-a)(\frac{-4}{16}-q)& =(\color{red}{-a}+\color{orange}{\frac{3}{20}}).(\color{green}{-q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{3}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{4}a-\frac{3}{20}q-\frac{3}{20}.\frac{1}{4}& \text{Uitwerken } \\ & =aq+\frac{1}{4}a-\frac{3}{20}q-\frac{3}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{7}{12})(a+\frac{11}{20})& =(\color{red}{a}+\color{orange}{\frac{-7}{12}}).(\color{green}{a}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{11}{20}a-\frac{7}{12}a-\frac{7}{12}.\frac{11}{20}& \text{Uitwerken } \\ & =a^2+(\frac{11}{20}+(\frac{-7}{12}))a-(\frac{-77}{240}) & \text{Neem samen} \\ &=a^2-\frac{2}{60}a-(\frac{-77}{240}) & \text{Maak de som} \\ &=a^2-\frac{1}{30}a+\frac{77}{240} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-2}{5})(\frac{-15}{6}-a)& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{-a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{2}x-\frac{2}{5}a-\frac{2}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =-ax-\frac{5}{2}x-\frac{2}{5}a-\frac{10}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{5}{2}x-\frac{2}{5}a-1 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{16}{11}-a)(\frac{-4}{7}+x)& =(\color{red}{-a}+\color{orange}{\frac{16}{11}}).(\color{green}{x}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{16}{11})} . \color{green}{(x)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{7}a+\frac{16}{11}x-\frac{16}{11}.\frac{4}{7}& \text{Uitwerken } \\ & =-ax+\frac{4}{7}a+\frac{16}{11}x-\frac{64}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{20}{12})(x-\frac{-20}{19})& =(\color{red}{q}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{20}{19}q-\frac{5}{3}x-\frac{5}{3}.\frac{20}{19}& \text{Uitwerken } \\ & =qx+\frac{20}{19}q-\frac{5}{3}x-\frac{100}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-18}{6}+q)(\frac{1}{17}+b)& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{17}q-3b-3.\frac{1}{17}& \text{Uitwerken } \\ & =bq+\frac{1}{17}q-3b-\frac{3}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{14}-b)(a+\frac{-10}{16})& =(\color{red}{-b}+\color{orange}{\frac{8}{7}}).(\color{green}{a}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{8}{7})} . \color{green}{(a)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{8}b+\frac{8}{7}a-\frac{8}{7}.\frac{5}{8}& \text{Uitwerken } \\ & =-ab+\frac{5}{8}b+\frac{8}{7}a-\frac{40}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{8}b+\frac{8}{7}a-\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{17}+x)(q-\frac{-4}{2})& =(\color{red}{x}+\color{orange}{\frac{-12}{17}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-12}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qx+2x-\frac{12}{17}q-\frac{12}{17}.2& \text{Uitwerken } \\ & =qx+2x-\frac{12}{17}q-\frac{24}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-5}{13})(a+\frac{6}{8})& =(\color{red}{a}+\color{orange}{\frac{-5}{13}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{4}a-\frac{5}{13}a-\frac{5}{13}.\frac{3}{4}& \text{Uitwerken } \\ & =a^2+(\frac{3}{4}+(\frac{-5}{13}))a-(\frac{-15}{52}) & \text{Neem samen} \\ &=a^2+\frac{19}{52}a-(\frac{-15}{52}) & \text{Maak de som} \\\end{align}\)
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