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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-17}{3}-p)(\frac{5}{4}-q)& =(\color{red}{-p}+\color{orange}{\frac{-17}{3}}).(\color{green}{-q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{4}p+\frac{17}{3}q-\frac{17}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =pq-\frac{5}{4}p+\frac{17}{3}q-\frac{85}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-7}{6})(\frac{12}{8}-p)& =(\color{red}{q}+\color{orange}{\frac{7}{6}}).(\color{green}{-p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{7}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{2}q-\frac{7}{6}p+\frac{7}{6}.\frac{3}{2}& \text{Uitwerken } \\ & =-pq+\frac{3}{2}q-\frac{7}{6}p+\frac{21}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{3}{2}q-\frac{7}{6}p+\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{14}-x)(x-\frac{5}{17})& =(\color{red}{-x}+\color{orange}{\frac{1}{14}}).(\color{green}{x}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{1}{14})} . \color{green}{(x)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{5}{17}x+\frac{1}{14}x-\frac{1}{14}.\frac{5}{17}& \text{Uitwerken } \\ & =-x^2+(\frac{5}{17}+\frac{1}{14})x-\frac{5}{238} & \text{Neem samen} \\ &=-x^2+\frac{87}{238}x-\frac{5}{238} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-5}{18})(q-\frac{-9}{12})& =(\color{red}{x}+\color{orange}{\frac{-5}{18}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{4}x-\frac{5}{18}q-\frac{5}{18}.\frac{3}{4}& \text{Uitwerken } \\ & =qx+\frac{3}{4}x-\frac{5}{18}q-\frac{15}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{3}{4}x-\frac{5}{18}q-\frac{5}{24} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{2}{18})(\frac{16}{12}+a)& =(\color{red}{a}+\color{orange}{\frac{-1}{9}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{3}a-\frac{1}{9}a-\frac{1}{9}.\frac{4}{3}& \text{Uitwerken } \\ & =a^2+(\frac{4}{3}+(\frac{-1}{9}))a-(\frac{-4}{27}) & \text{Neem samen} \\ &=a^2+\frac{11}{9}a-(\frac{-4}{27}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(b-\frac{2}{10})(\frac{13}{3}-x)& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{-x}+\color{blue}{\frac{13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{13}{3})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{13}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{13}{3}b+\frac{1}{5}x-\frac{1}{5}.\frac{13}{3}& \text{Uitwerken } \\ & =-bx+\frac{13}{3}b+\frac{1}{5}x-\frac{13}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-3}{6}+x)(x+\frac{-4}{11})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{4}{11}x-\frac{1}{2}x+\frac{1}{2}.\frac{4}{11}& \text{Uitwerken } \\ & =x^2+((\frac{-4}{11})+(\frac{-1}{2}))x+\frac{4}{22} & \text{Neem samen} \\ &=x^2-\frac{19}{22}x+\frac{4}{22} & \text{Maak de som} \\ &=x^2-\frac{19}{22}x+\frac{2}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(q+\frac{12}{3})(\frac{2}{16}+x)& =(\color{red}{q}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{8}q+4x+4.\frac{1}{8}& \text{Uitwerken } \\ & =qx+\frac{1}{8}q+4x+\frac{4}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{8}q+4x+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{17}{3})(\frac{13}{20}+p)& =(\color{red}{b}+\color{orange}{\frac{-17}{3}}).(\color{green}{p}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{20}b-\frac{17}{3}p-\frac{17}{3}.\frac{13}{20}& \text{Uitwerken } \\ & =bp+\frac{13}{20}b-\frac{17}{3}p-\frac{221}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{-7}{16})(a+\frac{20}{14})& =(\color{red}{x}+\color{orange}{\frac{-7}{16}}).(\color{green}{a}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{10}{7}x-\frac{7}{16}a-\frac{7}{16}.\frac{10}{7}& \text{Uitwerken } \\ & =ax+\frac{10}{7}x-\frac{7}{16}a-\frac{70}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{10}{7}x-\frac{7}{16}a-\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{8}{15})(p-\frac{-17}{12})& =(\color{red}{x}+\color{orange}{\frac{8}{15}}).(\color{green}{p}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{8}{15})} . \color{green}{(p)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{12}x+\frac{8}{15}p+\frac{8}{15}.\frac{17}{12}& \text{Uitwerken } \\ & =px+\frac{17}{12}x+\frac{8}{15}p+\frac{136}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{17}{12}x+\frac{8}{15}p+\frac{34}{45} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{15}{10}-x)(a-\frac{11}{2})& =(\color{red}{-x}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{11}{2}x+\frac{3}{2}a-\frac{3}{2}.\frac{11}{2}& \text{Uitwerken } \\ & =-ax+\frac{11}{2}x+\frac{3}{2}a-\frac{33}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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