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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{3}-x)(\frac{-12}{4}-q)& =(\color{red}{-x}+\color{orange}{\frac{20}{3}}).(\color{green}{-q}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{20}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = qx+3x-\frac{20}{3}q-\frac{20}{3}.3& \text{Uitwerken } \\ & =qx+3x-\frac{20}{3}q-\frac{60}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+3x-\frac{20}{3}q-20 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-15}{11}-p)(\frac{-5}{12}+q)& =(\color{red}{-p}+\color{orange}{\frac{-15}{11}}).(\color{green}{q}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{12}p-\frac{15}{11}q+\frac{15}{11}.\frac{5}{12}& \text{Uitwerken } \\ & =-pq+\frac{5}{12}p-\frac{15}{11}q+\frac{75}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{5}{12}p-\frac{15}{11}q+\frac{25}{44} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a+\frac{10}{12})((-9)+q)& =(\color{red}{a}+\color{orange}{\frac{5}{6}}).(\color{green}{q}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-9)} + \color{orange}{(\frac{5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = aq-9a+\frac{5}{6}q-\frac{5}{6}.9& \text{Uitwerken } \\ & =aq-9a+\frac{5}{6}q-\frac{45}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-9a+\frac{5}{6}q-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p+\frac{16}{3})(\frac{-5}{20}-a)& =(\color{red}{p}+\color{orange}{\frac{16}{3}}).(\color{green}{-a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{16}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{4}p-\frac{16}{3}a-\frac{16}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =-ap-\frac{1}{4}p-\frac{16}{3}a-\frac{16}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{1}{4}p-\frac{16}{3}a-\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-\frac{18}{19})(\frac{-1}{7}-x)& =(\color{red}{q}+\color{orange}{\frac{-18}{19}}).(\color{green}{-x}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{7}q+\frac{18}{19}x+\frac{18}{19}.\frac{1}{7}& \text{Uitwerken } \\ & =-qx-\frac{1}{7}q+\frac{18}{19}x+\frac{18}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{9}{3})(b-\frac{6}{18})& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{3}a-3b+3.\frac{1}{3}& \text{Uitwerken } \\ & =ab-\frac{1}{3}a-3b+\frac{3}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{3}a-3b+1 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{14}{11}+q)(a-\frac{3}{16})& =(\color{red}{q}+\color{orange}{\frac{14}{11}}).(\color{green}{a}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(\frac{14}{11})} . \color{green}{(a)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{16}q+\frac{14}{11}a-\frac{14}{11}.\frac{3}{16}& \text{Uitwerken } \\ & =aq-\frac{3}{16}q+\frac{14}{11}a-\frac{42}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{3}{16}q+\frac{14}{11}a-\frac{21}{88} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-7}{5})(\frac{-5}{14}-b)& =(\color{red}{a}+\color{orange}{\frac{7}{5}}).(\color{green}{-b}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{7}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{5}{14}a-\frac{7}{5}b-\frac{7}{5}.\frac{5}{14}& \text{Uitwerken } \\ & =-ab-\frac{5}{14}a-\frac{7}{5}b-\frac{35}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{5}{14}a-\frac{7}{5}b-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}((-11)-x)(q+(-20))& =(\color{red}{-x}+\color{orange}{(-11)}).(\color{green}{q}+\color{blue}{(-20)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-20)} + \color{orange}{(-11)} . \color{green}{(q)} + \color{orange}{(-11)} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = -qx+20x-11q+11.20& \text{Uitwerken } \\ & =-qx+20x-11q+220 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{5}{12})(\frac{-20}{11}-x)& =(\color{red}{x}+\color{orange}{\frac{-5}{12}}).(\color{green}{-x}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{20}{11}x+\frac{5}{12}x+\frac{5}{12}.\frac{20}{11}& \text{Uitwerken } \\ & =-x^2+((\frac{-20}{11})+\frac{5}{12})x+(\frac{-100}{132}) & \text{Neem samen} \\ &=-x^2-\frac{185}{132}x+(\frac{-100}{132}) & \text{Maak de som} \\ &=-x^2-\frac{185}{132}x+(\frac{-25}{33}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{2}{2}-q)(\frac{-9}{3}+q)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(-3)} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -qq+3q+1q-1.3& \text{Uitwerken } \\ & =-q^2+(3+1)q-3 & \text{Neem samen} \\ &=-q^2+4q-3 & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{3}-p)(\frac{3}{5}-p)& =(\color{red}{-p}+\color{orange}{(-5)}).(\color{green}{-p}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(-5)} . \color{green}{(-p)} + \color{orange}{(-5)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{5}p+5p-5.\frac{3}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{5})+5)p-(\frac{-15}{5}) & \text{Neem samen} \\ &=p^2+\frac{22}{5}p-(\frac{-15}{5}) & \text{Maak de som} \\ &=p^2+\frac{22}{5}p+3 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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