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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-14}{3}-x)(\frac{-20}{16}-a)& =(\color{red}{-x}+\color{orange}{\frac{-14}{3}}).(\color{green}{-a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{4}x+\frac{14}{3}a+\frac{14}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =ax+\frac{5}{4}x+\frac{14}{3}a+\frac{70}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{5}{4}x+\frac{14}{3}a+\frac{35}{6} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{15}{17})(q+\frac{6}{2})& =(\color{red}{b}+\color{orange}{\frac{15}{17}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{15}{17})} . \color{green}{(q)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bq+3b+\frac{15}{17}q+\frac{15}{17}.3& \text{Uitwerken } \\ & =bq+3b+\frac{15}{17}q+\frac{45}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{5}+x)(\frac{-10}{11}+p)& =(\color{red}{x}+\color{orange}{\frac{-14}{5}}).(\color{green}{p}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{11}x-\frac{14}{5}p+\frac{14}{5}.\frac{10}{11}& \text{Uitwerken } \\ & =px-\frac{10}{11}x-\frac{14}{5}p+\frac{140}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{10}{11}x-\frac{14}{5}p+\frac{28}{11} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a+\frac{14}{16})(\frac{15}{14}+b)& =(\color{red}{a}+\color{orange}{\frac{7}{8}}).(\color{green}{b}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{7}{8})} . \color{green}{(b)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{15}{14}a+\frac{7}{8}b+\frac{7}{8}.\frac{15}{14}& \text{Uitwerken } \\ & =ab+\frac{15}{14}a+\frac{7}{8}b+\frac{105}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{15}{14}a+\frac{7}{8}b+\frac{15}{16} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{11}+p)(p-\frac{8}{3})& =(\color{red}{p}+\color{orange}{\frac{-15}{11}}).(\color{green}{p}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{8}{3}p-\frac{15}{11}p+\frac{15}{11}.\frac{8}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-8}{3})+(\frac{-15}{11}))p+\frac{120}{33} & \text{Neem samen} \\ &=p^2-\frac{133}{33}p+\frac{120}{33} & \text{Maak de som} \\ &=p^2-\frac{133}{33}p+\frac{40}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-16}{18}-q)(p+\frac{-8}{12})& =(\color{red}{-q}+\color{orange}{\frac{-8}{9}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{2}{3}q-\frac{8}{9}p+\frac{8}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =-pq+\frac{2}{3}q-\frac{8}{9}p+\frac{16}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-3}{13}-q)(\frac{5}{12}+x)& =(\color{red}{-q}+\color{orange}{\frac{-3}{13}}).(\color{green}{x}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{12}q-\frac{3}{13}x-\frac{3}{13}.\frac{5}{12}& \text{Uitwerken } \\ & =-qx-\frac{5}{12}q-\frac{3}{13}x-\frac{15}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{5}{12}q-\frac{3}{13}x-\frac{5}{52} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-20}{20})(\frac{-9}{16}-q)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{9}{16}q+1q+1.\frac{9}{16}& \text{Uitwerken } \\ & =-q^2+((\frac{-9}{16})+1)q+(\frac{-9}{16}) & \text{Neem samen} \\ &=-q^2+\frac{7}{16}q+(\frac{-9}{16}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-9}{18}-x)(\frac{-13}{11}+b)& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{13}{11}x-\frac{1}{2}b+\frac{1}{2}.\frac{13}{11}& \text{Uitwerken } \\ & =-bx+\frac{13}{11}x-\frac{1}{2}b+\frac{13}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-3)(b-\frac{-9}{16})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{9}{16}b-3b-3.\frac{9}{16}& \text{Uitwerken } \\ & =b^2+(\frac{9}{16}+(-3))b-(\frac{-27}{16}) & \text{Neem samen} \\ &=b^2-\frac{39}{16}b-(\frac{-27}{16}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a+20)(\frac{-12}{17}+q)& =(\color{red}{a}+\color{orange}{20}).(\color{green}{q}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(20)} . \color{green}{(q)} + \color{orange}{(20)} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{12}{17}a+20q-20.\frac{12}{17}& \text{Uitwerken } \\ & =aq-\frac{12}{17}a+20q-\frac{240}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-18}{3})(q+\frac{8}{3})& =(\color{red}{q}+\color{orange}{(-6)}).(\color{green}{q}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(-6)} . \color{green}{(q)} + \color{orange}{(-6)} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{8}{3}q-6q-6.\frac{8}{3}& \text{Uitwerken } \\ & =q^2+(\frac{8}{3}+(-6))q-(\frac{-48}{3}) & \text{Neem samen} \\ &=q^2-\frac{10}{3}q-(\frac{-48}{3}) & \text{Maak de som} \\ &=q^2-\frac{10}{3}q+16 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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