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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{15}{4})(\frac{-8}{4}+q)& =(\color{red}{x}+\color{orange}{\frac{-15}{4}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-15}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2x-\frac{15}{4}q+\frac{15}{4}.2& \text{Uitwerken } \\ & =qx-2x-\frac{15}{4}q+\frac{30}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-2x-\frac{15}{4}q+\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{4}+a)(p-\frac{7}{3})& =(\color{red}{a}+\color{orange}{\frac{15}{4}}).(\color{green}{p}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{15}{4})} . \color{green}{(p)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{3}a+\frac{15}{4}p-\frac{15}{4}.\frac{7}{3}& \text{Uitwerken } \\ & =ap-\frac{7}{3}a+\frac{15}{4}p-\frac{105}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{7}{3}a+\frac{15}{4}p-\frac{35}{4} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{2}{12})(q+\frac{14}{4})& =(\color{red}{b}+\color{orange}{\frac{-1}{6}}).(\color{green}{q}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{2}b-\frac{1}{6}q-\frac{1}{6}.\frac{7}{2}& \text{Uitwerken } \\ & =bq+\frac{7}{2}b-\frac{1}{6}q-\frac{7}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-11}{19})(b+\frac{-3}{9})& =(\color{red}{a}+\color{orange}{\frac{-11}{19}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{3}a-\frac{11}{19}b+\frac{11}{19}.\frac{1}{3}& \text{Uitwerken } \\ & =ab-\frac{1}{3}a-\frac{11}{19}b+\frac{11}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{6}{9}+q)(q+\frac{19}{4})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{19}{4}q+\frac{2}{3}q+\frac{2}{3}.\frac{19}{4}& \text{Uitwerken } \\ & =q^2+(\frac{19}{4}+\frac{2}{3})q+\frac{38}{12} & \text{Neem samen} \\ &=q^2+\frac{65}{12}q+\frac{38}{12} & \text{Maak de som} \\ &=q^2+\frac{65}{12}q+\frac{19}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(p+2)(\frac{-11}{19}+b)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{19}p+2b-2.\frac{11}{19}& \text{Uitwerken } \\ & =bp-\frac{11}{19}p+2b-\frac{22}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-7}{16})(\frac{-18}{17}-p)& =(\color{red}{b}+\color{orange}{\frac{7}{16}}).(\color{green}{-p}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{7}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{18}{17}b-\frac{7}{16}p-\frac{7}{16}.\frac{18}{17}& \text{Uitwerken } \\ & =-bp-\frac{18}{17}b-\frac{7}{16}p-\frac{126}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{18}{17}b-\frac{7}{16}p-\frac{63}{136} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{5}{15})(\frac{-20}{5}+a)& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ap-4p+\frac{1}{3}a-\frac{1}{3}.4& \text{Uitwerken } \\ & =ap-4p+\frac{1}{3}a-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-18}{2}+b)(\frac{14}{2}-q)& =(\color{red}{b}+\color{orange}{(-9)}).(\color{green}{-q}+\color{blue}{7})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(7)} + \color{orange}{(-9)} . \color{green}{(-q)} + \color{orange}{(-9)} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -bq+7b+9q-9.7& \text{Uitwerken } \\ & =-bq+7b+9q-63 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{15}{17})(q-\frac{-20}{14})& =(\color{red}{a}+\color{orange}{\frac{-15}{17}}).(\color{green}{q}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{7}a-\frac{15}{17}q-\frac{15}{17}.\frac{10}{7}& \text{Uitwerken } \\ & =aq+\frac{10}{7}a-\frac{15}{17}q-\frac{150}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{18}{12}+a)(\frac{12}{17}-x)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{-x}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{12}{17}a-\frac{3}{2}x+\frac{3}{2}.\frac{12}{17}& \text{Uitwerken } \\ & =-ax+\frac{12}{17}a-\frac{3}{2}x+\frac{36}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{12}{17}a-\frac{3}{2}x+\frac{18}{17} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-1}{18})(\frac{-9}{7}+p)& =(\color{red}{x}+\color{orange}{\frac{1}{18}}).(\color{green}{p}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{1}{18})} . \color{green}{(p)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{7}x+\frac{1}{18}p-\frac{1}{18}.\frac{9}{7}& \text{Uitwerken } \\ & =px-\frac{9}{7}x+\frac{1}{18}p-\frac{9}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{9}{7}x+\frac{1}{18}p-\frac{1}{14} & \text{Vereenvoudig} \\\end{align}\)
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