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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{3}{5})(\frac{6}{12}-q)& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{-q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{1}{2}q+\frac{3}{5}q-\frac{3}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-q^2+(\frac{1}{2}+\frac{3}{5})q-\frac{3}{10} & \text{Neem samen} \\ &=-q^2+\frac{11}{10}q-\frac{3}{10} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-14}{7})(\frac{17}{10}+p)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{10}p+2p+2.\frac{17}{10}& \text{Uitwerken } \\ & =p^2+(\frac{17}{10}+2)p+\frac{34}{10} & \text{Neem samen} \\ &=p^2+\frac{37}{10}p+\frac{34}{10} & \text{Maak de som} \\ &=p^2+\frac{37}{10}p+\frac{17}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{15}{5}-q)(\frac{-18}{7}+q)& =(\color{red}{-q}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{18}{7}q+3q-3.\frac{18}{7}& \text{Uitwerken } \\ & =-q^2+(\frac{18}{7}+3)q-\frac{54}{7} & \text{Neem samen} \\ &=-q^2+\frac{39}{7}q-\frac{54}{7} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-14}{7})(\frac{18}{16}+b)& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{8}a-2b-2.\frac{9}{8}& \text{Uitwerken } \\ & =ab+\frac{9}{8}a-2b-\frac{18}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{9}{8}a-2b-\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x-\frac{4}{2})(x-\frac{5}{6})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{5}{6}x-2x+2.\frac{5}{6}& \text{Uitwerken } \\ & =x^2+((\frac{-5}{6})+(-2))x+\frac{10}{6} & \text{Neem samen} \\ &=x^2-\frac{17}{6}x+\frac{10}{6} & \text{Maak de som} \\ &=x^2-\frac{17}{6}x+\frac{5}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{19}+q)(\frac{18}{3}-a)& =(\color{red}{q}+\color{orange}{\frac{-4}{19}}).(\color{green}{-a}+\color{blue}{6})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(\frac{-4}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -aq+6q+\frac{4}{19}a-\frac{4}{19}.6& \text{Uitwerken } \\ & =-aq+6q+\frac{4}{19}a-\frac{24}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{2}{15}-q)(b-(-11))& =(\color{red}{-q}+\color{orange}{\frac{2}{15}}).(\color{green}{b}+\color{blue}{11})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(11)} + \color{orange}{(\frac{2}{15})} . \color{green}{(b)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = -bq-11q+\frac{2}{15}b+\frac{2}{15}.11& \text{Uitwerken } \\ & =-bq-11q+\frac{2}{15}b+\frac{22}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{6}{4})(p-\frac{-18}{14})& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{7}x+\frac{3}{2}p+\frac{3}{2}.\frac{9}{7}& \text{Uitwerken } \\ & =px+\frac{9}{7}x+\frac{3}{2}p+\frac{27}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{11}{8})(\frac{-20}{14}-q)& =(\color{red}{x}+\color{orange}{\frac{-11}{8}}).(\color{green}{-q}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{10}{7}x+\frac{11}{8}q+\frac{11}{8}.\frac{10}{7}& \text{Uitwerken } \\ & =-qx-\frac{10}{7}x+\frac{11}{8}q+\frac{110}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{10}{7}x+\frac{11}{8}q+\frac{55}{28} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-18}{17})(\frac{8}{12}+q)& =(\color{red}{p}+\color{orange}{\frac{18}{17}}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{18}{17})} . \color{green}{(q)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{3}p+\frac{18}{17}q+\frac{18}{17}.\frac{2}{3}& \text{Uitwerken } \\ & =pq+\frac{2}{3}p+\frac{18}{17}q+\frac{36}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{2}{3}p+\frac{18}{17}q+\frac{12}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b+\frac{8}{18})(x+\frac{-8}{12})& =(\color{red}{b}+\color{orange}{\frac{4}{9}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{3}b+\frac{4}{9}x-\frac{4}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =bx-\frac{2}{3}b+\frac{4}{9}x-\frac{8}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-4}{4}+x)(\frac{-2}{10}-q)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{5}x+1q+1.\frac{1}{5}& \text{Uitwerken } \\ & =-qx-\frac{1}{5}x+1q+\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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