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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{15}{7})(p-\frac{7}{20})& =(\color{red}{b}+\color{orange}{\frac{-15}{7}}).(\color{green}{p}+\color{blue}{\frac{-7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{20})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{-7}{20})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{20}b-\frac{15}{7}p+\frac{15}{7}.\frac{7}{20}& \text{Uitwerken } \\ & =bp-\frac{7}{20}b-\frac{15}{7}p+\frac{105}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{7}{20}b-\frac{15}{7}p+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q-\frac{1}{16})(x-\frac{-12}{15})& =(\color{red}{q}+\color{orange}{\frac{-1}{16}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{5}q-\frac{1}{16}x-\frac{1}{16}.\frac{4}{5}& \text{Uitwerken } \\ & =qx+\frac{4}{5}q-\frac{1}{16}x-\frac{4}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{4}{5}q-\frac{1}{16}x-\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{8}+x)(q-\frac{19}{2})& =(\color{red}{x}+\color{orange}{\frac{-7}{4}}).(\color{green}{q}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{2}x-\frac{7}{4}q+\frac{7}{4}.\frac{19}{2}& \text{Uitwerken } \\ & =qx-\frac{19}{2}x-\frac{7}{4}q+\frac{133}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{5}{2}-x)(b+\frac{8}{16})& =(\color{red}{-x}+\color{orange}{\frac{5}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{2}x+\frac{5}{2}b+\frac{5}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =-bx-\frac{1}{2}x+\frac{5}{2}b+\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{6}+q)(b+(-16))& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{(-16)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-16)} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = bq-16q+\frac{2}{3}b-\frac{2}{3}.16& \text{Uitwerken } \\ & =bq-16q+\frac{2}{3}b-\frac{32}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{14}{4}+b)(\frac{-10}{15}+b)& =(\color{red}{b}+\color{orange}{\frac{7}{2}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{2}{3}b+\frac{7}{2}b-\frac{7}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-2}{3})+\frac{7}{2})b-(\frac{-14}{6}) & \text{Neem samen} \\ &=b^2+\frac{17}{6}b-(\frac{-14}{6}) & \text{Maak de som} \\ &=b^2+\frac{17}{6}b+\frac{7}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-11}{18}-p)(b+\frac{-17}{15})& =(\color{red}{-p}+\color{orange}{\frac{-11}{18}}).(\color{green}{b}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{15}p-\frac{11}{18}b+\frac{11}{18}.\frac{17}{15}& \text{Uitwerken } \\ & =-bp+\frac{17}{15}p-\frac{11}{18}b+\frac{187}{270} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{20}{17}-q)(\frac{-17}{19}-b)& =(\color{red}{-q}+\color{orange}{\frac{20}{17}}).(\color{green}{-b}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{20}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{20}{17})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{19}q-\frac{20}{17}b-\frac{20}{17}.\frac{17}{19}& \text{Uitwerken } \\ & =bq+\frac{17}{19}q-\frac{20}{17}b-\frac{340}{323} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{17}{19}q-\frac{20}{17}b-\frac{20}{19} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-5}{2})(p+\frac{15}{20})& =(\color{red}{x}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{4}x-\frac{5}{2}p-\frac{5}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =px+\frac{3}{4}x-\frac{5}{2}p-\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-20}{9})(\frac{2}{11}-x)& =(\color{red}{x}+\color{orange}{\frac{20}{9}}).(\color{green}{-x}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{20}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{2}{11}x-\frac{20}{9}x+\frac{20}{9}.\frac{2}{11}& \text{Uitwerken } \\ & =-x^2+(\frac{2}{11}+(\frac{-20}{9}))x+(\frac{-40}{99}) & \text{Neem samen} \\ &=-x^2-\frac{202}{99}x+(\frac{-40}{99}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-2}{20}+a)(\frac{2}{3}-a)& =(\color{red}{a}+\color{orange}{\frac{-1}{10}}).(\color{green}{-a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{2}{3}a+\frac{1}{10}a-\frac{1}{10}.\frac{2}{3}& \text{Uitwerken } \\ & =-a^2+(\frac{2}{3}+\frac{1}{10})a-\frac{2}{30} & \text{Neem samen} \\ &=-a^2+\frac{23}{30}a-\frac{2}{30} & \text{Maak de som} \\ &=-a^2+\frac{23}{30}a-\frac{1}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{15}{8}+a)(\frac{-15}{14}-a)& =(\color{red}{a}+\color{orange}{\frac{15}{8}}).(\color{green}{-a}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{15}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{15}{14}a-\frac{15}{8}a-\frac{15}{8}.\frac{15}{14}& \text{Uitwerken } \\ & =-a^2+((\frac{-15}{14})+(\frac{-15}{8}))a-\frac{225}{112} & \text{Neem samen} \\ &=-a^2-\frac{165}{56}a-\frac{225}{112} & \text{Maak de som} \\\end{align}\)
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