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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-1}{16})(\frac{-18}{12}-q)& =(\color{red}{p}+\color{orange}{\frac{-1}{16}}).(\color{green}{-q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{2}p+\frac{1}{16}q+\frac{1}{16}.\frac{3}{2}& \text{Uitwerken } \\ & =-pq-\frac{3}{2}p+\frac{1}{16}q+\frac{3}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{18}{13})(x-\frac{-20}{4})& =(\color{red}{a}+\color{orange}{\frac{-18}{13}}).(\color{green}{x}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(5)} + \color{orange}{(\frac{-18}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ax+5a-\frac{18}{13}x-\frac{18}{13}.5& \text{Uitwerken } \\ & =ax+5a-\frac{18}{13}x-\frac{90}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-12}{2})(\frac{16}{13}+p)& =(\color{red}{b}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{16}{13}b-6p-6.\frac{16}{13}& \text{Uitwerken } \\ & =bp+\frac{16}{13}b-6p-\frac{96}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{20}{10})(\frac{-3}{17}+x)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{17}x-2x+2.\frac{3}{17}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{17})+(-2))x+\frac{6}{17} & \text{Neem samen} \\ &=x^2-\frac{37}{17}x+\frac{6}{17} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-18}{14})(x-\frac{17}{10})& =(\color{red}{b}+\color{orange}{\frac{-9}{7}}).(\color{green}{x}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{10}b-\frac{9}{7}x+\frac{9}{7}.\frac{17}{10}& \text{Uitwerken } \\ & =bx-\frac{17}{10}b-\frac{9}{7}x+\frac{153}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-18}{13})(\frac{2}{9}-a)& =(\color{red}{a}+\color{orange}{\frac{18}{13}}).(\color{green}{-a}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{18}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{2}{9}a-\frac{18}{13}a+\frac{18}{13}.\frac{2}{9}& \text{Uitwerken } \\ & =-a^2+(\frac{2}{9}+(\frac{-18}{13}))a+(\frac{-36}{117}) & \text{Neem samen} \\ &=-a^2-\frac{136}{117}a+(\frac{-36}{117}) & \text{Maak de som} \\ &=-a^2-\frac{136}{117}a+(\frac{-4}{13}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{3}{16}+b)(\frac{5}{12}-p)& =(\color{red}{b}+\color{orange}{\frac{3}{16}}).(\color{green}{-p}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{3}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{12}b-\frac{3}{16}p+\frac{3}{16}.\frac{5}{12}& \text{Uitwerken } \\ & =-bp+\frac{5}{12}b-\frac{3}{16}p+\frac{15}{192} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{5}{12}b-\frac{3}{16}p+\frac{5}{64} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{8}{10})(\frac{7}{5}+a)& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{a}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{5}b+\frac{4}{5}a+\frac{4}{5}.\frac{7}{5}& \text{Uitwerken } \\ & =ab+\frac{7}{5}b+\frac{4}{5}a+\frac{28}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{3}{8})(\frac{-9}{8}-a)& =(\color{red}{b}+\color{orange}{\frac{-3}{8}}).(\color{green}{-a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{9}{8}b+\frac{3}{8}a+\frac{3}{8}.\frac{9}{8}& \text{Uitwerken } \\ & =-ab-\frac{9}{8}b+\frac{3}{8}a+\frac{27}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-12}{14})(q-\frac{-17}{10})& =(\color{red}{q}+\color{orange}{\frac{-6}{7}}).(\color{green}{q}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{17}{10}q-\frac{6}{7}q-\frac{6}{7}.\frac{17}{10}& \text{Uitwerken } \\ & =q^2+(\frac{17}{10}+(\frac{-6}{7}))q-(\frac{-102}{70}) & \text{Neem samen} \\ &=q^2+\frac{59}{70}q-(\frac{-102}{70}) & \text{Maak de som} \\ &=q^2+\frac{59}{70}q+\frac{51}{35} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(p-\frac{10}{16})(b+\frac{13}{14})& =(\color{red}{p}+\color{orange}{\frac{-5}{8}}).(\color{green}{b}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{14}p-\frac{5}{8}b-\frac{5}{8}.\frac{13}{14}& \text{Uitwerken } \\ & =bp+\frac{13}{14}p-\frac{5}{8}b-\frac{65}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-17}{4})(b-\frac{-20}{10})& =(\color{red}{p}+\color{orange}{\frac{17}{4}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{17}{4})} . \color{green}{(b)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bp+2p+\frac{17}{4}b+\frac{17}{4}.2& \text{Uitwerken } \\ & =bp+2p+\frac{17}{4}b+\frac{34}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+2p+\frac{17}{4}b+\frac{17}{2} & \text{Vereenvoudig} \\\end{align}\)
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