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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{19}+x)(\frac{-18}{6}+b)& =(\color{red}{x}+\color{orange}{\frac{20}{19}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{20}{19})} . \color{green}{(b)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bx-3x+\frac{20}{19}b-\frac{20}{19}.3& \text{Uitwerken } \\ & =bx-3x+\frac{20}{19}b-\frac{60}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-2}{8})(b-\frac{-4}{17})& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{17}p-\frac{1}{4}b-\frac{1}{4}.\frac{4}{17}& \text{Uitwerken } \\ & =bp+\frac{4}{17}p-\frac{1}{4}b-\frac{4}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{4}{17}p-\frac{1}{4}b-\frac{1}{17} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-20}{13})(q+\frac{10}{18})& =(\color{red}{x}+\color{orange}{\frac{-20}{13}}).(\color{green}{q}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{9}x-\frac{20}{13}q-\frac{20}{13}.\frac{5}{9}& \text{Uitwerken } \\ & =qx+\frac{5}{9}x-\frac{20}{13}q-\frac{100}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{13}{3}+p)(\frac{-5}{2}-a)& =(\color{red}{p}+\color{orange}{\frac{13}{3}}).(\color{green}{-a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{13}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{2}p-\frac{13}{3}a-\frac{13}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =-ap-\frac{5}{2}p-\frac{13}{3}a-\frac{65}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{3}{13}-q)(b-\frac{7}{17})& =(\color{red}{-q}+\color{orange}{\frac{3}{13}}).(\color{green}{b}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{3}{13})} . \color{green}{(b)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{17}q+\frac{3}{13}b-\frac{3}{13}.\frac{7}{17}& \text{Uitwerken } \\ & =-bq+\frac{7}{17}q+\frac{3}{13}b-\frac{21}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-13}{3})(a-\frac{18}{14})& =(\color{red}{p}+\color{orange}{\frac{13}{3}}).(\color{green}{a}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{13}{3})} . \color{green}{(a)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{7}p+\frac{13}{3}a-\frac{13}{3}.\frac{9}{7}& \text{Uitwerken } \\ & =ap-\frac{9}{7}p+\frac{13}{3}a-\frac{117}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{9}{7}p+\frac{13}{3}a-\frac{39}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{12}{6}+x)(\frac{-19}{4}-p)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-p}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(2)} . \color{green}{(-p)} + \color{orange}{(2)} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{4}x-2p-2.\frac{19}{4}& \text{Uitwerken } \\ & =-px-\frac{19}{4}x-2p-\frac{38}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{19}{4}x-2p-\frac{19}{2} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{19}-x)(q+\frac{-18}{6})& =(\color{red}{-x}+\color{orange}{\frac{-3}{19}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-3}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -qx+3x-\frac{3}{19}q+\frac{3}{19}.3& \text{Uitwerken } \\ & =-qx+3x-\frac{3}{19}q+\frac{9}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{2}{20})(\frac{-18}{14}-b)& =(\color{red}{a}+\color{orange}{\frac{1}{10}}).(\color{green}{-b}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{1}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{9}{7}a-\frac{1}{10}b-\frac{1}{10}.\frac{9}{7}& \text{Uitwerken } \\ & =-ab-\frac{9}{7}a-\frac{1}{10}b-\frac{9}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{7}{12}+x)(\frac{-18}{9}-p)& =(\color{red}{x}+\color{orange}{\frac{7}{12}}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{7}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -px-2x-\frac{7}{12}p-\frac{7}{12}.2& \text{Uitwerken } \\ & =-px-2x-\frac{7}{12}p-\frac{14}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-2x-\frac{7}{12}p-\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b-\frac{11}{7})(q-\frac{-9}{3})& =(\color{red}{b}+\color{orange}{\frac{-11}{7}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{-11}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bq+3b-\frac{11}{7}q-\frac{11}{7}.3& \text{Uitwerken } \\ & =bq+3b-\frac{11}{7}q-\frac{33}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{2}{12})(\frac{4}{8}-b)& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{-b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{1}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{2}a-\frac{1}{6}b+\frac{1}{6}.\frac{1}{2}& \text{Uitwerken } \\ & =-ab+\frac{1}{2}a-\frac{1}{6}b+\frac{1}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 01:38:20