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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{6}{12})(a-\frac{-6}{5})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{5}q+\frac{1}{2}a+\frac{1}{2}.\frac{6}{5}& \text{Uitwerken } \\ & =aq+\frac{6}{5}q+\frac{1}{2}a+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{6}{5}q+\frac{1}{2}a+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{7}+a)(a+\frac{11}{8})& =(\color{red}{a}+\color{orange}{\frac{20}{7}}).(\color{green}{a}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{20}{7})} . \color{green}{(a)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{11}{8}a+\frac{20}{7}a+\frac{20}{7}.\frac{11}{8}& \text{Uitwerken } \\ & =a^2+(\frac{11}{8}+\frac{20}{7})a+\frac{220}{56} & \text{Neem samen} \\ &=a^2+\frac{237}{56}a+\frac{220}{56} & \text{Maak de som} \\ &=a^2+\frac{237}{56}a+\frac{55}{14} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(b-\frac{18}{8})(\frac{14}{16}+a)& =(\color{red}{b}+\color{orange}{\frac{-9}{4}}).(\color{green}{a}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{8}b-\frac{9}{4}a-\frac{9}{4}.\frac{7}{8}& \text{Uitwerken } \\ & =ab+\frac{7}{8}b-\frac{9}{4}a-\frac{63}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{8}{19})(b+\frac{15}{15})& =(\color{red}{q}+\color{orange}{\frac{8}{19}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{8}{19})} . \color{green}{(b)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q+\frac{8}{19}b+\frac{8}{19}.1& \text{Uitwerken } \\ & =bq+1q+\frac{8}{19}b+\frac{8}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{6}{3})(p-\frac{10}{11})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{11}x-2p+2.\frac{10}{11}& \text{Uitwerken } \\ & =px-\frac{10}{11}x-2p+\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{17}{15})(\frac{-8}{14}-b)& =(\color{red}{x}+\color{orange}{\frac{-17}{15}}).(\color{green}{-b}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{7}x+\frac{17}{15}b+\frac{17}{15}.\frac{4}{7}& \text{Uitwerken } \\ & =-bx-\frac{4}{7}x+\frac{17}{15}b+\frac{68}{105} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-6}{10}-q)(p+\frac{-5}{6})& =(\color{red}{-q}+\color{orange}{\frac{-3}{5}}).(\color{green}{p}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{6}q-\frac{3}{5}p+\frac{3}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =-pq+\frac{5}{6}q-\frac{3}{5}p+\frac{15}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{5}{6}q-\frac{3}{5}p+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{1}{14}+q)(\frac{8}{15}-a)& =(\color{red}{q}+\color{orange}{\frac{1}{14}}).(\color{green}{-a}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{1}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{8}{15}q-\frac{1}{14}a+\frac{1}{14}.\frac{8}{15}& \text{Uitwerken } \\ & =-aq+\frac{8}{15}q-\frac{1}{14}a+\frac{8}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{8}{15}q-\frac{1}{14}a+\frac{4}{105} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-12}{17})(a-(-1))& =(\color{red}{a}+\color{orange}{\frac{12}{17}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aa+1a+\frac{12}{17}a+\frac{12}{17}.1& \text{Uitwerken } \\ & =a^2+(1+\frac{12}{17})a+\frac{12}{17} & \text{Neem samen} \\ &=a^2+\frac{29}{17}a+\frac{12}{17} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-17}{7})(p-\frac{-17}{4})& =(\color{red}{p}+\color{orange}{\frac{-17}{7}}).(\color{green}{p}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{-17}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{4}p-\frac{17}{7}p-\frac{17}{7}.\frac{17}{4}& \text{Uitwerken } \\ & =p^2+(\frac{17}{4}+(\frac{-17}{7}))p-(\frac{-289}{28}) & \text{Neem samen} \\ &=p^2+\frac{51}{28}p-(\frac{-289}{28}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-2}{2}+p)(x+\frac{-20}{19})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{20}{19}p-1x+1.\frac{20}{19}& \text{Uitwerken } \\ & =px-\frac{20}{19}p-1x+\frac{20}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-16}{15})(\frac{5}{16}+b)& =(\color{red}{a}+\color{orange}{\frac{-16}{15}}).(\color{green}{b}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{16}a-\frac{16}{15}b-\frac{16}{15}.\frac{5}{16}& \text{Uitwerken } \\ & =ab+\frac{5}{16}a-\frac{16}{15}b-\frac{80}{240} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{5}{16}a-\frac{16}{15}b-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
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