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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-13}{3})(\frac{-1}{7}-x)& =(\color{red}{p}+\color{orange}{\frac{13}{3}}).(\color{green}{-x}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{13}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{7}p-\frac{13}{3}x-\frac{13}{3}.\frac{1}{7}& \text{Uitwerken } \\ & =-px-\frac{1}{7}p-\frac{13}{3}x-\frac{13}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{5}-p)(b+\frac{10}{15})& =(\color{red}{-p}+\color{orange}{\frac{19}{5}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{19}{5})} . \color{green}{(b)} + \color{orange}{(\frac{19}{5})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{2}{3}p+\frac{19}{5}b+\frac{19}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =-bp-\frac{2}{3}p+\frac{19}{5}b+\frac{38}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{19}{4})((-19)-b)& =(\color{red}{x}+\color{orange}{\frac{19}{4}}).(\color{green}{-b}+\color{blue}{(-19)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(-19)} + \color{orange}{(\frac{19}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = -bx-19x-\frac{19}{4}b-\frac{19}{4}.19& \text{Uitwerken } \\ & =-bx-19x-\frac{19}{4}b-\frac{361}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{17}{10})(p+\frac{-2}{20})& =(\color{red}{p}+\color{orange}{\frac{-17}{10}}).(\color{green}{p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{10}p-\frac{17}{10}p+\frac{17}{10}.\frac{1}{10}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{10})+(\frac{-17}{10}))p+\frac{17}{100} & \text{Neem samen} \\ &=p^2-\frac{18}{10}p+\frac{17}{100} & \text{Maak de som} \\ &=p^2-\frac{9}{5}p+\frac{17}{100} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{7}+x)(\frac{-10}{10}+q)& =(\color{red}{x}+\color{orange}{\frac{-15}{7}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-15}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1x-\frac{15}{7}q+\frac{15}{7}.1& \text{Uitwerken } \\ & =qx-1x-\frac{15}{7}q+\frac{15}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{12}{7}+p)(q-\frac{-7}{13})& =(\color{red}{p}+\color{orange}{\frac{12}{7}}).(\color{green}{q}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{12}{7})} . \color{green}{(q)} + \color{orange}{(\frac{12}{7})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{13}p+\frac{12}{7}q+\frac{12}{7}.\frac{7}{13}& \text{Uitwerken } \\ & =pq+\frac{7}{13}p+\frac{12}{7}q+\frac{84}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{7}{13}p+\frac{12}{7}q+\frac{12}{13} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x+\frac{7}{9})(q-\frac{-7}{14})& =(\color{red}{x}+\color{orange}{\frac{7}{9}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}x+\frac{7}{9}q+\frac{7}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}x+\frac{7}{9}q+\frac{7}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-15}{7}-b)(\frac{7}{16}+x)& =(\color{red}{-b}+\color{orange}{\frac{-15}{7}}).(\color{green}{x}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{7}{16}b-\frac{15}{7}x-\frac{15}{7}.\frac{7}{16}& \text{Uitwerken } \\ & =-bx-\frac{7}{16}b-\frac{15}{7}x-\frac{105}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{7}{16}b-\frac{15}{7}x-\frac{15}{16} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{17}{2}+p)(\frac{4}{12}+q)& =(\color{red}{p}+\color{orange}{\frac{17}{2}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{17}{2})} . \color{green}{(q)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{3}p+\frac{17}{2}q+\frac{17}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =pq+\frac{1}{3}p+\frac{17}{2}q+\frac{17}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{11}{4})(a-\frac{11}{6})& =(\color{red}{p}+\color{orange}{\frac{-11}{4}}).(\color{green}{a}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{-11}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{4})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{6}p-\frac{11}{4}a+\frac{11}{4}.\frac{11}{6}& \text{Uitwerken } \\ & =ap-\frac{11}{6}p-\frac{11}{4}a+\frac{121}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{19}{14}+q)(p+\frac{14}{3})& =(\color{red}{q}+\color{orange}{\frac{19}{14}}).(\color{green}{p}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{19}{14})} . \color{green}{(p)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{14}{3}q+\frac{19}{14}p+\frac{19}{14}.\frac{14}{3}& \text{Uitwerken } \\ & =pq+\frac{14}{3}q+\frac{19}{14}p+\frac{266}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{14}{3}q+\frac{19}{14}p+\frac{19}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-(-20))(\frac{-19}{8}-a)& =(\color{red}{b}+\color{orange}{20}).(\color{green}{-a}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(20)} . \color{green}{(-a)} + \color{orange}{(20)} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{19}{8}b-20a-20.\frac{19}{8}& \text{Uitwerken } \\ & =-ab-\frac{19}{8}b-20a-\frac{380}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{19}{8}b-20a-\frac{95}{2} & \text{Vereenvoudig} \\\end{align}\)
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