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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{1}{10}-b)(\frac{5}{18}-x)& =(\color{red}{-b}+\color{orange}{\frac{1}{10}}).(\color{green}{-x}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{1}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{18}b-\frac{1}{10}x+\frac{1}{10}.\frac{5}{18}& \text{Uitwerken } \\ & =bx-\frac{5}{18}b-\frac{1}{10}x+\frac{5}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{5}{18}b-\frac{1}{10}x+\frac{1}{36} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-6}{11})(q-\frac{-9}{10})& =(\color{red}{a}+\color{orange}{\frac{-6}{11}}).(\color{green}{q}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{10}a-\frac{6}{11}q-\frac{6}{11}.\frac{9}{10}& \text{Uitwerken } \\ & =aq+\frac{9}{10}a-\frac{6}{11}q-\frac{54}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{9}{10}a-\frac{6}{11}q-\frac{27}{55} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-6}{9})(\frac{-12}{12}-a)& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ax-1x+\frac{2}{3}a+\frac{2}{3}.1& \text{Uitwerken } \\ & =-ax-1x+\frac{2}{3}a+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{-7}{8})(b+\frac{-3}{18})& =(\color{red}{b}+\color{orange}{\frac{7}{8}}).(\color{green}{b}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{7}{8})} . \color{green}{(b)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{6}b+\frac{7}{8}b-\frac{7}{8}.\frac{1}{6}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{6})+\frac{7}{8})b-(\frac{-7}{48}) & \text{Neem samen} \\ &=b^2+\frac{17}{24}b-(\frac{-7}{48}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-15}{7})(\frac{-14}{13}+b)& =(\color{red}{p}+\color{orange}{\frac{15}{7}}).(\color{green}{b}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{15}{7})} . \color{green}{(b)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{14}{13}p+\frac{15}{7}b-\frac{15}{7}.\frac{14}{13}& \text{Uitwerken } \\ & =bp-\frac{14}{13}p+\frac{15}{7}b-\frac{210}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{14}{13}p+\frac{15}{7}b-\frac{30}{13} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{18}{15})(\frac{7}{17}-x)& =(\color{red}{b}+\color{orange}{\frac{-6}{5}}).(\color{green}{-x}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{17}b+\frac{6}{5}x-\frac{6}{5}.\frac{7}{17}& \text{Uitwerken } \\ & =-bx+\frac{7}{17}b+\frac{6}{5}x-\frac{42}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-(-11))(\frac{-16}{15}-a)& =(\color{red}{q}+\color{orange}{11}).(\color{green}{-a}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(11)} . \color{green}{(-a)} + \color{orange}{(11)} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{16}{15}q-11a-11.\frac{16}{15}& \text{Uitwerken } \\ & =-aq-\frac{16}{15}q-11a-\frac{176}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{17}+q)(\frac{-4}{8}-a)& =(\color{red}{q}+\color{orange}{\frac{18}{17}}).(\color{green}{-a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{18}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{2}q-\frac{18}{17}a-\frac{18}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =-aq-\frac{1}{2}q-\frac{18}{17}a-\frac{18}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{1}{2}q-\frac{18}{17}a-\frac{9}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{10}{7}+x)(\frac{10}{3}-b)& =(\color{red}{x}+\color{orange}{\frac{10}{7}}).(\color{green}{-b}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{10}{3}x-\frac{10}{7}b+\frac{10}{7}.\frac{10}{3}& \text{Uitwerken } \\ & =-bx+\frac{10}{3}x-\frac{10}{7}b+\frac{100}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{8}{18})(\frac{-17}{12}+q)& =(\color{red}{a}+\color{orange}{\frac{-4}{9}}).(\color{green}{q}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{12}a-\frac{4}{9}q+\frac{4}{9}.\frac{17}{12}& \text{Uitwerken } \\ & =aq-\frac{17}{12}a-\frac{4}{9}q+\frac{68}{108} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{17}{12}a-\frac{4}{9}q+\frac{17}{27} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p+\frac{18}{4})(x+(-8))& =(\color{red}{p}+\color{orange}{\frac{9}{2}}).(\color{green}{x}+\color{blue}{(-8)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-8)} + \color{orange}{(\frac{9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = px-8p+\frac{9}{2}x-\frac{9}{2}.8& \text{Uitwerken } \\ & =px-8p+\frac{9}{2}x-\frac{72}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-8p+\frac{9}{2}x-36 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{10}{4}-q)(\frac{10}{12}+q)& =(\color{red}{-q}+\color{orange}{\frac{5}{2}}).(\color{green}{q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{5}{6}q+\frac{5}{2}q+\frac{5}{2}.\frac{5}{6}& \text{Uitwerken } \\ & =-q^2+((\frac{-5}{6})+\frac{5}{2})q+(\frac{-25}{12}) & \text{Neem samen} \\ &=-q^2+\frac{10}{6}q+(\frac{-25}{12}) & \text{Maak de som} \\ &=-q^2+\frac{5}{3}q+(\frac{-25}{12}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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