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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{17}{3}-a)(a+\frac{9}{6})& =(\color{red}{-a}+\color{orange}{\frac{17}{3}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{17}{3})} . \color{green}{(a)} + \color{orange}{(\frac{17}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{3}{2}a+\frac{17}{3}a+\frac{17}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-3}{2})+\frac{17}{3})a+(\frac{-51}{6}) & \text{Neem samen} \\ &=-a^2+\frac{25}{6}a+(\frac{-51}{6}) & \text{Maak de som} \\ &=-a^2+\frac{25}{6}a+(\frac{-17}{2}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{1}{20}+q)(\frac{3}{4}+x)& =(\color{red}{q}+\color{orange}{\frac{1}{20}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{1}{20})} . \color{green}{(x)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{4}q+\frac{1}{20}x+\frac{1}{20}.\frac{3}{4}& \text{Uitwerken } \\ & =qx+\frac{3}{4}q+\frac{1}{20}x+\frac{3}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{8}{2})(\frac{10}{10}+x)& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = xx+1x-4x-4.1& \text{Uitwerken } \\ & =x^2+(1+(-4))x-(-4) & \text{Neem samen} \\ &=x^2-3x-(-4) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-18}{5})(\frac{-15}{5}+q)& =(\color{red}{a}+\color{orange}{\frac{18}{5}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{18}{5})} . \color{green}{(q)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = aq-3a+\frac{18}{5}q-\frac{18}{5}.3& \text{Uitwerken } \\ & =aq-3a+\frac{18}{5}q-\frac{54}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{19}+b)(a+\frac{-1}{13})& =(\color{red}{b}+\color{orange}{\frac{-16}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{13}b-\frac{16}{19}a+\frac{16}{19}.\frac{1}{13}& \text{Uitwerken } \\ & =ab-\frac{1}{13}b-\frac{16}{19}a+\frac{16}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-13}{17})(x-\frac{4}{20})& =(\color{red}{a}+\color{orange}{\frac{-13}{17}}).(\color{green}{x}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{5}a-\frac{13}{17}x+\frac{13}{17}.\frac{1}{5}& \text{Uitwerken } \\ & =ax-\frac{1}{5}a-\frac{13}{17}x+\frac{13}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-15}{4}+x)(\frac{14}{18}-p)& =(\color{red}{x}+\color{orange}{\frac{-15}{4}}).(\color{green}{-p}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{9}x+\frac{15}{4}p-\frac{15}{4}.\frac{7}{9}& \text{Uitwerken } \\ & =-px+\frac{7}{9}x+\frac{15}{4}p-\frac{105}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{7}{9}x+\frac{15}{4}p-\frac{35}{12} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{2}{7}-x)(\frac{19}{16}-q)& =(\color{red}{-x}+\color{orange}{\frac{2}{7}}).(\color{green}{-q}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{2}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{16}x-\frac{2}{7}q+\frac{2}{7}.\frac{19}{16}& \text{Uitwerken } \\ & =qx-\frac{19}{16}x-\frac{2}{7}q+\frac{38}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{19}{16}x-\frac{2}{7}q+\frac{19}{56} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{10}{3})(b-\frac{7}{10})& =(\color{red}{p}+\color{orange}{\frac{-10}{3}}).(\color{green}{b}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{10}p-\frac{10}{3}b+\frac{10}{3}.\frac{7}{10}& \text{Uitwerken } \\ & =bp-\frac{7}{10}p-\frac{10}{3}b+\frac{70}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{7}{10}p-\frac{10}{3}b+\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{8}-b)(\frac{4}{3}+a)& =(\color{red}{-b}+\color{orange}{\frac{5}{4}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{3}b+\frac{5}{4}a+\frac{5}{4}.\frac{4}{3}& \text{Uitwerken } \\ & =-ab-\frac{4}{3}b+\frac{5}{4}a+\frac{20}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{4}{3}b+\frac{5}{4}a+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{2}{4}-a)(\frac{3}{8}-q)& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{-q}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{8}a-\frac{1}{2}q+\frac{1}{2}.\frac{3}{8}& \text{Uitwerken } \\ & =aq-\frac{3}{8}a-\frac{1}{2}q+\frac{3}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{12}{17})(a+\frac{16}{3})& =(\color{red}{x}+\color{orange}{\frac{12}{17}}).(\color{green}{a}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{16}{3}x+\frac{12}{17}a+\frac{12}{17}.\frac{16}{3}& \text{Uitwerken } \\ & =ax+\frac{16}{3}x+\frac{12}{17}a+\frac{192}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{16}{3}x+\frac{12}{17}a+\frac{64}{17} & \text{Vereenvoudig} \\\end{align}\)
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