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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-17}{18})(a-\frac{-12}{17})& =(\color{red}{q}+\color{orange}{\frac{17}{18}}).(\color{green}{a}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{17}{18})} . \color{green}{(a)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{12}{17}q+\frac{17}{18}a+\frac{17}{18}.\frac{12}{17}& \text{Uitwerken } \\ & =aq+\frac{12}{17}q+\frac{17}{18}a+\frac{204}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{12}{17}q+\frac{17}{18}a+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-4}{3}+b)(q+\frac{18}{16})& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{8}b-\frac{4}{3}q-\frac{4}{3}.\frac{9}{8}& \text{Uitwerken } \\ & =bq+\frac{9}{8}b-\frac{4}{3}q-\frac{36}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{9}{8}b-\frac{4}{3}q-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{10}{12}-x)(b-\frac{5}{18})& =(\color{red}{-x}+\color{orange}{\frac{5}{6}}).(\color{green}{b}+\color{blue}{\frac{-5}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{18})} + \color{orange}{(\frac{5}{6})} . \color{green}{(b)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-5}{18})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{18}x+\frac{5}{6}b-\frac{5}{6}.\frac{5}{18}& \text{Uitwerken } \\ & =-bx+\frac{5}{18}x+\frac{5}{6}b-\frac{25}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{7}{12})(\frac{10}{15}-b)& =(\color{red}{a}+\color{orange}{\frac{-7}{12}}).(\color{green}{-b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{3}a+\frac{7}{12}b-\frac{7}{12}.\frac{2}{3}& \text{Uitwerken } \\ & =-ab+\frac{2}{3}a+\frac{7}{12}b-\frac{14}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{2}{3}a+\frac{7}{12}b-\frac{7}{18} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-4}{2}-p)(\frac{-17}{20}+x)& =(\color{red}{-p}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{17}{20}p-2x+2.\frac{17}{20}& \text{Uitwerken } \\ & =-px+\frac{17}{20}p-2x+\frac{34}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{17}{20}p-2x+\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{2}+q)(\frac{17}{11}+p)& =(\color{red}{q}+\color{orange}{(-7)}).(\color{green}{p}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(-7)} . \color{green}{(p)} + \color{orange}{(-7)} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{17}{11}q-7p-7.\frac{17}{11}& \text{Uitwerken } \\ & =pq+\frac{17}{11}q-7p-\frac{119}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-16}{15})(\frac{14}{14}-a)& =(\color{red}{b}+\color{orange}{\frac{-16}{15}}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-16}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ab+1b+\frac{16}{15}a-\frac{16}{15}.1& \text{Uitwerken } \\ & =-ab+1b+\frac{16}{15}a-\frac{16}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-1}{10})(\frac{-17}{16}-a)& =(\color{red}{p}+\color{orange}{\frac{-1}{10}}).(\color{green}{-a}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{16}p+\frac{1}{10}a+\frac{1}{10}.\frac{17}{16}& \text{Uitwerken } \\ & =-ap-\frac{17}{16}p+\frac{1}{10}a+\frac{17}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-18}{12})(\frac{15}{3}+a)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ax+5x+\frac{3}{2}a+\frac{3}{2}.5& \text{Uitwerken } \\ & =ax+5x+\frac{3}{2}a+\frac{15}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-10}{9}+b)(x-\frac{-7}{4})& =(\color{red}{b}+\color{orange}{\frac{-10}{9}}).(\color{green}{x}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{4}b-\frac{10}{9}x-\frac{10}{9}.\frac{7}{4}& \text{Uitwerken } \\ & =bx+\frac{7}{4}b-\frac{10}{9}x-\frac{70}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{7}{4}b-\frac{10}{9}x-\frac{35}{18} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{10}+a)(\frac{20}{3}-x)& =(\color{red}{a}+\color{orange}{\frac{8}{5}}).(\color{green}{-x}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{8}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{20}{3}a-\frac{8}{5}x+\frac{8}{5}.\frac{20}{3}& \text{Uitwerken } \\ & =-ax+\frac{20}{3}a-\frac{8}{5}x+\frac{160}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{20}{3}a-\frac{8}{5}x+\frac{32}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-20}{7})(\frac{-3}{19}+a)& =(\color{red}{a}+\color{orange}{\frac{-20}{7}}).(\color{green}{a}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{19}a-\frac{20}{7}a+\frac{20}{7}.\frac{3}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{19})+(\frac{-20}{7}))a+\frac{60}{133} & \text{Neem samen} \\ &=a^2-\frac{401}{133}a+\frac{60}{133} & \text{Maak de som} \\\end{align}\)
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