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

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  1. \((\frac{-19}{15}+x)(\frac{5}{6}+q)\)
  2. \((\frac{-7}{18}+x)(q-\frac{-16}{15})\)
  3. \((\frac{-11}{13}+x)(\frac{-18}{15}-p)\)
  4. \((\frac{-16}{13}-a)(a-\frac{-17}{7})\)
  5. \((x+\frac{-13}{17})(\frac{-14}{10}+a)\)
  6. \((\frac{-2}{20}+a)(\frac{13}{14}+a)\)
  7. \((\frac{-20}{2}-x)(x-\frac{-17}{3})\)
  8. \((\frac{-3}{3}-b)(\frac{-17}{20}-x)\)
  9. \((a+\frac{16}{8})(\frac{11}{3}-a)\)
  10. \((\frac{9}{18}-q)(p-\frac{8}{18})\)
  11. \((b-(-12))(\frac{15}{5}-b)\)
  12. \((\frac{2}{10}+x)(q-\frac{-5}{4})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{15}+x)(\frac{5}{6}+q)& =(\color{red}{x}+\color{orange}{\frac{-19}{15}}).(\color{green}{q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{6}x-\frac{19}{15}q-\frac{19}{15}.\frac{5}{6}& \text{Uitwerken } \\ & =qx+\frac{5}{6}x-\frac{19}{15}q-\frac{95}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{5}{6}x-\frac{19}{15}q-\frac{19}{18} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-7}{18}+x)(q-\frac{-16}{15})& =(\color{red}{x}+\color{orange}{\frac{-7}{18}}).(\color{green}{q}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{16}{15}x-\frac{7}{18}q-\frac{7}{18}.\frac{16}{15}& \text{Uitwerken } \\ & =qx+\frac{16}{15}x-\frac{7}{18}q-\frac{112}{270} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{16}{15}x-\frac{7}{18}q-\frac{56}{135} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{13}+x)(\frac{-18}{15}-p)& =(\color{red}{x}+\color{orange}{\frac{-11}{13}}).(\color{green}{-p}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{6}{5}x+\frac{11}{13}p+\frac{11}{13}.\frac{6}{5}& \text{Uitwerken } \\ & =-px-\frac{6}{5}x+\frac{11}{13}p+\frac{66}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-16}{13}-a)(a-\frac{-17}{7})& =(\color{red}{-a}+\color{orange}{\frac{-16}{13}}).(\color{green}{a}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{17}{7}a-\frac{16}{13}a-\frac{16}{13}.\frac{17}{7}& \text{Uitwerken } \\ & =-a^2+((\frac{-17}{7})+(\frac{-16}{13}))a-\frac{272}{91} & \text{Neem samen} \\ &=-a^2-\frac{333}{91}a-\frac{272}{91} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-13}{17})(\frac{-14}{10}+a)& =(\color{red}{x}+\color{orange}{\frac{-13}{17}}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{5}x-\frac{13}{17}a+\frac{13}{17}.\frac{7}{5}& \text{Uitwerken } \\ & =ax-\frac{7}{5}x-\frac{13}{17}a+\frac{91}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-2}{20}+a)(\frac{13}{14}+a)& =(\color{red}{a}+\color{orange}{\frac{-1}{10}}).(\color{green}{a}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{13}{14}a-\frac{1}{10}a-\frac{1}{10}.\frac{13}{14}& \text{Uitwerken } \\ & =a^2+(\frac{13}{14}+(\frac{-1}{10}))a-(\frac{-13}{140}) & \text{Neem samen} \\ &=a^2+\frac{58}{70}a-(\frac{-13}{140}) & \text{Maak de som} \\ &=a^2+\frac{29}{35}a+\frac{13}{140} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-20}{2}-x)(x-\frac{-17}{3})& =(\color{red}{-x}+\color{orange}{(-10)}).(\color{green}{x}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(-10)} . \color{green}{(x)} + \color{orange}{(-10)} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{17}{3}x-10x-10.\frac{17}{3}& \text{Uitwerken } \\ & =-x^2+((\frac{-17}{3})+(-10))x-\frac{170}{3} & \text{Neem samen} \\ &=-x^2-\frac{47}{3}x-\frac{170}{3} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{3}-b)(\frac{-17}{20}-x)& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{20}b+1x+1.\frac{17}{20}& \text{Uitwerken } \\ & =bx+\frac{17}{20}b+1x+\frac{17}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{16}{8})(\frac{11}{3}-a)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{-a}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(2)} . \color{green}{(-a)} + \color{orange}{(2)} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{11}{3}a-2a+2.\frac{11}{3}& \text{Uitwerken } \\ & =-a^2+(\frac{11}{3}+(-2))a+(\frac{-22}{3}) & \text{Neem samen} \\ &=-a^2+\frac{5}{3}a+(\frac{-22}{3}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{9}{18}-q)(p-\frac{8}{18})& =(\color{red}{-q}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{4}{9}q+\frac{1}{2}p-\frac{1}{2}.\frac{4}{9}& \text{Uitwerken } \\ & =-pq+\frac{4}{9}q+\frac{1}{2}p-\frac{4}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{4}{9}q+\frac{1}{2}p-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b-(-12))(\frac{15}{5}-b)& =(\color{red}{b}+\color{orange}{12}).(\color{green}{-b}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(12)} . \color{green}{(-b)} + \color{orange}{(12)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -bb+3b-12b+12.3& \text{Uitwerken } \\ & =-b^2+(3+(-12))b+(-36) & \text{Neem samen} \\ &=-b^2-9b+(-36) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{2}{10}+x)(q-\frac{-5}{4})& =(\color{red}{x}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{4}x+\frac{1}{5}q+\frac{1}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =qx+\frac{5}{4}x+\frac{1}{5}q+\frac{5}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{5}{4}x+\frac{1}{5}q+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
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