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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{14}-q)(\frac{-2}{4}+x)& =(\color{red}{-q}+\color{orange}{\frac{11}{14}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{11}{14})} . \color{green}{(x)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{2}q+\frac{11}{14}x-\frac{11}{14}.\frac{1}{2}& \text{Uitwerken } \\ & =-qx+\frac{1}{2}q+\frac{11}{14}x-\frac{11}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-13}{7})(\frac{10}{18}+a)& =(\color{red}{b}+\color{orange}{\frac{-13}{7}}).(\color{green}{a}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{9}b-\frac{13}{7}a-\frac{13}{7}.\frac{5}{9}& \text{Uitwerken } \\ & =ab+\frac{5}{9}b-\frac{13}{7}a-\frac{65}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-2}{6}+x)(\frac{3}{14}+q)& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{14}x-\frac{1}{3}q-\frac{1}{3}.\frac{3}{14}& \text{Uitwerken } \\ & =qx+\frac{3}{14}x-\frac{1}{3}q-\frac{3}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{3}{14}x-\frac{1}{3}q-\frac{1}{14} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b+\frac{15}{4})(x+\frac{17}{12})& =(\color{red}{b}+\color{orange}{\frac{15}{4}}).(\color{green}{x}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{15}{4})} . \color{green}{(x)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{12}b+\frac{15}{4}x+\frac{15}{4}.\frac{17}{12}& \text{Uitwerken } \\ & =bx+\frac{17}{12}b+\frac{15}{4}x+\frac{255}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{17}{12}b+\frac{15}{4}x+\frac{85}{16} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{7}-b)(b+\frac{-14}{13})& =(\color{red}{-b}+\color{orange}{\frac{-3}{7}}).(\color{green}{b}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{14}{13}b-\frac{3}{7}b+\frac{3}{7}.\frac{14}{13}& \text{Uitwerken } \\ & =-b^2+(\frac{14}{13}+(\frac{-3}{7}))b+(\frac{-42}{91}) & \text{Neem samen} \\ &=-b^2+\frac{59}{91}b+(\frac{-42}{91}) & \text{Maak de som} \\ &=-b^2+\frac{59}{91}b+(\frac{-6}{13}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-11}{5})(\frac{-2}{10}-x)& =(\color{red}{q}+\color{orange}{\frac{-11}{5}}).(\color{green}{-x}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{5}q+\frac{11}{5}x+\frac{11}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =-qx-\frac{1}{5}q+\frac{11}{5}x+\frac{11}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{6}-q)(\frac{-15}{9}-x)& =(\color{red}{-q}+\color{orange}{(-3)}).(\color{green}{-x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(-3)} . \color{green}{(-x)} + \color{orange}{(-3)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{3}q+3x+3.\frac{5}{3}& \text{Uitwerken } \\ & =qx+\frac{5}{3}q+3x+\frac{15}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{5}{3}q+3x+5 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-10}{9}+a)(p-\frac{2}{7})& =(\color{red}{a}+\color{orange}{\frac{-10}{9}}).(\color{green}{p}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{7}a-\frac{10}{9}p+\frac{10}{9}.\frac{2}{7}& \text{Uitwerken } \\ & =ap-\frac{2}{7}a-\frac{10}{9}p+\frac{20}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-4}{9}+p)(\frac{10}{7}-b)& =(\color{red}{p}+\color{orange}{\frac{-4}{9}}).(\color{green}{-b}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{10}{7}p+\frac{4}{9}b-\frac{4}{9}.\frac{10}{7}& \text{Uitwerken } \\ & =-bp+\frac{10}{7}p+\frac{4}{9}b-\frac{40}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-10}{12})(q+\frac{17}{14})& =(\color{red}{q}+\color{orange}{\frac{5}{6}}).(\color{green}{q}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{17}{14}q+\frac{5}{6}q+\frac{5}{6}.\frac{17}{14}& \text{Uitwerken } \\ & =q^2+(\frac{17}{14}+\frac{5}{6})q+\frac{85}{84} & \text{Neem samen} \\ &=q^2+\frac{86}{42}q+\frac{85}{84} & \text{Maak de som} \\ &=q^2+\frac{43}{21}q+\frac{85}{84} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-2}{12}-x)(4+q)& =(\color{red}{-x}+\color{orange}{\frac{-1}{6}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(4)} + \color{orange}{(\frac{-1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -qx-4x-\frac{1}{6}q-\frac{1}{6}.4& \text{Uitwerken } \\ & =-qx-4x-\frac{1}{6}q-\frac{4}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-4x-\frac{1}{6}q-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{20}-a)(\frac{5}{3}-x)& =(\color{red}{-a}+\color{orange}{\frac{2}{5}}).(\color{green}{-x}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{3}a-\frac{2}{5}x+\frac{2}{5}.\frac{5}{3}& \text{Uitwerken } \\ & =ax-\frac{5}{3}a-\frac{2}{5}x+\frac{10}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{3}a-\frac{2}{5}x+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
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