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

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  1. \((a-\frac{17}{19})(p+(-15))\)
  2. \((\frac{6}{16}-q)(\frac{13}{12}-a)\)
  3. \((\frac{-14}{18}+x)(\frac{-4}{19}+q)\)
  4. \((q+\frac{-15}{4})(\frac{2}{10}-q)\)
  5. \((\frac{4}{19}-x)(p+\frac{7}{6})\)
  6. \((\frac{-18}{18}+p)(b+\frac{17}{5})\)
  7. \((\frac{-13}{6}-b)(\frac{-13}{3}+x)\)
  8. \((\frac{18}{13}-a)(x-\frac{5}{10})\)
  9. \((x+\frac{16}{7})(\frac{1}{11}-q)\)
  10. \((p-\frac{-15}{14})(x-\frac{17}{12})\)
  11. \((q+\frac{9}{14})(\frac{14}{10}-a)\)
  12. \((\frac{-10}{18}+b)(\frac{-18}{20}-p)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{17}{19})(p+(-15))& =(\color{red}{a}+\color{orange}{\frac{-17}{19}}).(\color{green}{p}+\color{blue}{(-15)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-15)} + \color{orange}{(\frac{-17}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = ap-15a-\frac{17}{19}p+\frac{17}{19}.15& \text{Uitwerken } \\ & =ap-15a-\frac{17}{19}p+\frac{255}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{6}{16}-q)(\frac{13}{12}-a)& =(\color{red}{-q}+\color{orange}{\frac{3}{8}}).(\color{green}{-a}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{3}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{12}q-\frac{3}{8}a+\frac{3}{8}.\frac{13}{12}& \text{Uitwerken } \\ & =aq-\frac{13}{12}q-\frac{3}{8}a+\frac{39}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{13}{12}q-\frac{3}{8}a+\frac{13}{32} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{18}+x)(\frac{-4}{19}+q)& =(\color{red}{x}+\color{orange}{\frac{-7}{9}}).(\color{green}{q}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{19}x-\frac{7}{9}q+\frac{7}{9}.\frac{4}{19}& \text{Uitwerken } \\ & =qx-\frac{4}{19}x-\frac{7}{9}q+\frac{28}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-15}{4})(\frac{2}{10}-q)& =(\color{red}{q}+\color{orange}{\frac{-15}{4}}).(\color{green}{-q}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{1}{5}q+\frac{15}{4}q-\frac{15}{4}.\frac{1}{5}& \text{Uitwerken } \\ & =-q^2+(\frac{1}{5}+\frac{15}{4})q-\frac{15}{20} & \text{Neem samen} \\ &=-q^2+\frac{79}{20}q-\frac{15}{20} & \text{Maak de som} \\ &=-q^2+\frac{79}{20}q-\frac{3}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{19}-x)(p+\frac{7}{6})& =(\color{red}{-x}+\color{orange}{\frac{4}{19}}).(\color{green}{p}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{4}{19})} . \color{green}{(p)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{6}x+\frac{4}{19}p+\frac{4}{19}.\frac{7}{6}& \text{Uitwerken } \\ & =-px-\frac{7}{6}x+\frac{4}{19}p+\frac{28}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{7}{6}x+\frac{4}{19}p+\frac{14}{57} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-18}{18}+p)(b+\frac{17}{5})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{17}{5}p-1b-1.\frac{17}{5}& \text{Uitwerken } \\ & =bp+\frac{17}{5}p-1b-\frac{17}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-13}{6}-b)(\frac{-13}{3}+x)& =(\color{red}{-b}+\color{orange}{\frac{-13}{6}}).(\color{green}{x}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{13}{3}b-\frac{13}{6}x+\frac{13}{6}.\frac{13}{3}& \text{Uitwerken } \\ & =-bx+\frac{13}{3}b-\frac{13}{6}x+\frac{169}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{13}-a)(x-\frac{5}{10})& =(\color{red}{-a}+\color{orange}{\frac{18}{13}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{18}{13})} . \color{green}{(x)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{2}a+\frac{18}{13}x-\frac{18}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =-ax+\frac{1}{2}a+\frac{18}{13}x-\frac{18}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{1}{2}a+\frac{18}{13}x-\frac{9}{13} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{16}{7})(\frac{1}{11}-q)& =(\color{red}{x}+\color{orange}{\frac{16}{7}}).(\color{green}{-q}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{16}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{11}x-\frac{16}{7}q+\frac{16}{7}.\frac{1}{11}& \text{Uitwerken } \\ & =-qx+\frac{1}{11}x-\frac{16}{7}q+\frac{16}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-15}{14})(x-\frac{17}{12})& =(\color{red}{p}+\color{orange}{\frac{15}{14}}).(\color{green}{x}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{15}{14})} . \color{green}{(x)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{12}p+\frac{15}{14}x-\frac{15}{14}.\frac{17}{12}& \text{Uitwerken } \\ & =px-\frac{17}{12}p+\frac{15}{14}x-\frac{255}{168} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{17}{12}p+\frac{15}{14}x-\frac{85}{56} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{9}{14})(\frac{14}{10}-a)& =(\color{red}{q}+\color{orange}{\frac{9}{14}}).(\color{green}{-a}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{9}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{5}q-\frac{9}{14}a+\frac{9}{14}.\frac{7}{5}& \text{Uitwerken } \\ & =-aq+\frac{7}{5}q-\frac{9}{14}a+\frac{63}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{7}{5}q-\frac{9}{14}a+\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{18}+b)(\frac{-18}{20}-p)& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{-p}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{9}{10}b+\frac{5}{9}p+\frac{5}{9}.\frac{9}{10}& \text{Uitwerken } \\ & =-bp-\frac{9}{10}b+\frac{5}{9}p+\frac{45}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{9}{10}b+\frac{5}{9}p+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
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