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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{18}{6}-a)(p+\frac{-3}{16})& =(\color{red}{-a}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{16}a+3p-3.\frac{3}{16}& \text{Uitwerken } \\ & =-ap+\frac{3}{16}a+3p-\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{9}-q)(\frac{-20}{13}-x)& =(\color{red}{-q}+\color{orange}{\frac{5}{3}}).(\color{green}{-x}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{20}{13}q-\frac{5}{3}x-\frac{5}{3}.\frac{20}{13}& \text{Uitwerken } \\ & =qx+\frac{20}{13}q-\frac{5}{3}x-\frac{100}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-7}{9})(\frac{-6}{10}+q)& =(\color{red}{p}+\color{orange}{\frac{7}{9}}).(\color{green}{q}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{5}p+\frac{7}{9}q-\frac{7}{9}.\frac{3}{5}& \text{Uitwerken } \\ & =pq-\frac{3}{5}p+\frac{7}{9}q-\frac{21}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{3}{5}p+\frac{7}{9}q-\frac{7}{15} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-15}{12}-x)(b-\frac{-10}{15})& =(\color{red}{-x}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{2}{3}x-\frac{5}{4}b-\frac{5}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =-bx-\frac{2}{3}x-\frac{5}{4}b-\frac{10}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{2}{3}x-\frac{5}{4}b-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q+\frac{14}{5})(\frac{5}{8}+p)& =(\color{red}{q}+\color{orange}{\frac{14}{5}}).(\color{green}{p}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{14}{5})} . \color{green}{(p)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{8}q+\frac{14}{5}p+\frac{14}{5}.\frac{5}{8}& \text{Uitwerken } \\ & =pq+\frac{5}{8}q+\frac{14}{5}p+\frac{70}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{8}q+\frac{14}{5}p+\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{9}{6}-a)(q-\frac{-12}{3})& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(4)} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -aq-4a+\frac{3}{2}q+\frac{3}{2}.4& \text{Uitwerken } \\ & =-aq-4a+\frac{3}{2}q+\frac{12}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-4a+\frac{3}{2}q+6 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-8}{15})(\frac{1}{9}+q)& =(\color{red}{p}+\color{orange}{\frac{8}{15}}).(\color{green}{q}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{8}{15})} . \color{green}{(q)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{9}p+\frac{8}{15}q+\frac{8}{15}.\frac{1}{9}& \text{Uitwerken } \\ & =pq+\frac{1}{9}p+\frac{8}{15}q+\frac{8}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-10}{10}-a)(b-\frac{-6}{17})& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{6}{17}a-1b-1.\frac{6}{17}& \text{Uitwerken } \\ & =-ab-\frac{6}{17}a-1b-\frac{6}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-17}{11})(\frac{-1}{16}-b)& =(\color{red}{b}+\color{orange}{\frac{17}{11}}).(\color{green}{-b}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{17}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{16}b-\frac{17}{11}b-\frac{17}{11}.\frac{1}{16}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{16})+(\frac{-17}{11}))b-\frac{17}{176} & \text{Neem samen} \\ &=-b^2-\frac{283}{176}b-\frac{17}{176} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-17}{9}-q)(p-\frac{-14}{19})& =(\color{red}{-q}+\color{orange}{\frac{-17}{9}}).(\color{green}{p}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{14}{19}q-\frac{17}{9}p-\frac{17}{9}.\frac{14}{19}& \text{Uitwerken } \\ & =-pq-\frac{14}{19}q-\frac{17}{9}p-\frac{238}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{18}{13})(\frac{-19}{16}-b)& =(\color{red}{q}+\color{orange}{\frac{-18}{13}}).(\color{green}{-b}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{-18}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{19}{16}q+\frac{18}{13}b+\frac{18}{13}.\frac{19}{16}& \text{Uitwerken } \\ & =-bq-\frac{19}{16}q+\frac{18}{13}b+\frac{342}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{19}{16}q+\frac{18}{13}b+\frac{171}{104} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-5}{18})(q-\frac{9}{7})& =(\color{red}{x}+\color{orange}{\frac{5}{18}}).(\color{green}{q}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{5}{18})} . \color{green}{(q)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{7}x+\frac{5}{18}q-\frac{5}{18}.\frac{9}{7}& \text{Uitwerken } \\ & =qx-\frac{9}{7}x+\frac{5}{18}q-\frac{45}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{9}{7}x+\frac{5}{18}q-\frac{5}{14} & \text{Vereenvoudig} \\\end{align}\)
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