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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-12}{10}+q)(x-\frac{12}{13})& =(\color{red}{q}+\color{orange}{\frac{-6}{5}}).(\color{green}{x}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{12}{13}q-\frac{6}{5}x+\frac{6}{5}.\frac{12}{13}& \text{Uitwerken } \\ & =qx-\frac{12}{13}q-\frac{6}{5}x+\frac{72}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-3}{11})(b+\frac{1}{3})& =(\color{red}{a}+\color{orange}{\frac{-3}{11}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{3}a-\frac{3}{11}b-\frac{3}{11}.\frac{1}{3}& \text{Uitwerken } \\ & =ab+\frac{1}{3}a-\frac{3}{11}b-\frac{3}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{3}a-\frac{3}{11}b-\frac{1}{11} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{20}{12}+q)(q-\frac{-8}{13})& =(\color{red}{q}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{8}{13}q+\frac{5}{3}q+\frac{5}{3}.\frac{8}{13}& \text{Uitwerken } \\ & =q^2+(\frac{8}{13}+\frac{5}{3})q+\frac{40}{39} & \text{Neem samen} \\ &=q^2+\frac{89}{39}q+\frac{40}{39} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-9}{15}-a)(p-\frac{-18}{9})& =(\color{red}{-a}+\color{orange}{\frac{-3}{5}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(\frac{-3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ap-2a-\frac{3}{5}p-\frac{3}{5}.2& \text{Uitwerken } \\ & =-ap-2a-\frac{3}{5}p-\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-18}{5}+x)(\frac{-3}{4}-x)& =(\color{red}{x}+\color{orange}{\frac{-18}{5}}).(\color{green}{-x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{3}{4}x+\frac{18}{5}x+\frac{18}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =-x^2+((\frac{-3}{4})+\frac{18}{5})x+(\frac{-54}{20}) & \text{Neem samen} \\ &=-x^2+\frac{57}{20}x+(\frac{-54}{20}) & \text{Maak de som} \\ &=-x^2+\frac{57}{20}x+(\frac{-27}{10}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{11}{2}-b)(q-\frac{-16}{19})& =(\color{red}{-b}+\color{orange}{\frac{11}{2}}).(\color{green}{q}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{11}{2})} . \color{green}{(q)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{16}{19}b+\frac{11}{2}q+\frac{11}{2}.\frac{16}{19}& \text{Uitwerken } \\ & =-bq-\frac{16}{19}b+\frac{11}{2}q+\frac{176}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{16}{19}b+\frac{11}{2}q+\frac{88}{19} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-13}{14})(b-\frac{16}{5})& =(\color{red}{x}+\color{orange}{\frac{13}{14}}).(\color{green}{b}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{13}{14})} . \color{green}{(b)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{16}{5}x+\frac{13}{14}b-\frac{13}{14}.\frac{16}{5}& \text{Uitwerken } \\ & =bx-\frac{16}{5}x+\frac{13}{14}b-\frac{208}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{16}{5}x+\frac{13}{14}b-\frac{104}{35} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-14}{9})(p-\frac{-12}{20})& =(\color{red}{p}+\color{orange}{\frac{-14}{9}}).(\color{green}{p}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{3}{5}p-\frac{14}{9}p-\frac{14}{9}.\frac{3}{5}& \text{Uitwerken } \\ & =p^2+(\frac{3}{5}+(\frac{-14}{9}))p-(\frac{-42}{45}) & \text{Neem samen} \\ &=p^2-\frac{43}{45}p-(\frac{-42}{45}) & \text{Maak de som} \\ &=p^2-\frac{43}{45}p+\frac{14}{15} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{3}{3}+a)(a-\frac{5}{8})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{8}a+1a-1.\frac{5}{8}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{8})+1)a-(\frac{-5}{8}) & \text{Neem samen} \\ &=a^2+\frac{3}{8}a-(\frac{-5}{8}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{20}{3}+q)(p-\frac{-20}{19})& =(\color{red}{q}+\color{orange}{\frac{20}{3}}).(\color{green}{p}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{20}{3})} . \color{green}{(p)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{20}{19}q+\frac{20}{3}p+\frac{20}{3}.\frac{20}{19}& \text{Uitwerken } \\ & =pq+\frac{20}{19}q+\frac{20}{3}p+\frac{400}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{7}{11}+p)(a+\frac{18}{12})& =(\color{red}{p}+\color{orange}{\frac{7}{11}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{7}{11})} . \color{green}{(a)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{2}p+\frac{7}{11}a+\frac{7}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =ap+\frac{3}{2}p+\frac{7}{11}a+\frac{21}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{4}-q)(p+\frac{-1}{7})& =(\color{red}{-q}+\color{orange}{\frac{13}{4}}).(\color{green}{p}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{13}{4})} . \color{green}{(p)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{7}q+\frac{13}{4}p-\frac{13}{4}.\frac{1}{7}& \text{Uitwerken } \\ & =-pq+\frac{1}{7}q+\frac{13}{4}p-\frac{13}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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