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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-8}{9})(\frac{-13}{19}-x)& =(\color{red}{a}+\color{orange}{\frac{8}{9}}).(\color{green}{-x}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{8}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{13}{19}a-\frac{8}{9}x-\frac{8}{9}.\frac{13}{19}& \text{Uitwerken } \\ & =-ax-\frac{13}{19}a-\frac{8}{9}x-\frac{104}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{18}{7})((-4)+b)& =(\color{red}{x}+\color{orange}{\frac{18}{7}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{18}{7})} . \color{green}{(b)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bx-4x+\frac{18}{7}b-\frac{18}{7}.4& \text{Uitwerken } \\ & =bx-4x+\frac{18}{7}b-\frac{72}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-13}{9})(\frac{10}{13}-b)& =(\color{red}{a}+\color{orange}{\frac{13}{9}}).(\color{green}{-b}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(\frac{13}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{10}{13}a-\frac{13}{9}b+\frac{13}{9}.\frac{10}{13}& \text{Uitwerken } \\ & =-ab+\frac{10}{13}a-\frac{13}{9}b+\frac{130}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{10}{13}a-\frac{13}{9}b+\frac{10}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-13}{15}+x)(\frac{1}{8}+b)& =(\color{red}{x}+\color{orange}{\frac{-13}{15}}).(\color{green}{b}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{8}x-\frac{13}{15}b-\frac{13}{15}.\frac{1}{8}& \text{Uitwerken } \\ & =bx+\frac{1}{8}x-\frac{13}{15}b-\frac{13}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-19}{14})(\frac{19}{13}+p)& =(\color{red}{b}+\color{orange}{\frac{-19}{14}}).(\color{green}{p}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{13}b-\frac{19}{14}p-\frac{19}{14}.\frac{19}{13}& \text{Uitwerken } \\ & =bp+\frac{19}{13}b-\frac{19}{14}p-\frac{361}{182} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{9}-q)(x+\frac{-9}{15})& =(\color{red}{-q}+\color{orange}{\frac{20}{9}}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{20}{9})} . \color{green}{(x)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{5}q+\frac{20}{9}x-\frac{20}{9}.\frac{3}{5}& \text{Uitwerken } \\ & =-qx+\frac{3}{5}q+\frac{20}{9}x-\frac{60}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{3}{5}q+\frac{20}{9}x-\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-19}{18}-p)(p-\frac{-4}{20})& =(\color{red}{-p}+\color{orange}{\frac{-19}{18}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{5}p-\frac{19}{18}p-\frac{19}{18}.\frac{1}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{5})+(\frac{-19}{18}))p-\frac{19}{90} & \text{Neem samen} \\ &=-p^2-\frac{113}{90}p-\frac{19}{90} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}((-8)-q)(\frac{-1}{6}-p)& =(\color{red}{-q}+\color{orange}{(-8)}).(\color{green}{-p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(-8)} . \color{green}{(-p)} + \color{orange}{(-8)} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{6}q+8p+8.\frac{1}{6}& \text{Uitwerken } \\ & =pq+\frac{1}{6}q+8p+\frac{8}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{6}q+8p+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{9}{10}-p)(a+\frac{-7}{14})& =(\color{red}{-p}+\color{orange}{\frac{9}{10}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{9}{10})} . \color{green}{(a)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{2}p+\frac{9}{10}a-\frac{9}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =-ap+\frac{1}{2}p+\frac{9}{10}a-\frac{9}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-2}{7})(a+\frac{15}{7})& =(\color{red}{b}+\color{orange}{\frac{-2}{7}}).(\color{green}{a}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{15}{7}b-\frac{2}{7}a-\frac{2}{7}.\frac{15}{7}& \text{Uitwerken } \\ & =ab+\frac{15}{7}b-\frac{2}{7}a-\frac{30}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-12}{19})(\frac{-13}{2}+x)& =(\color{red}{q}+\color{orange}{\frac{-12}{19}}).(\color{green}{x}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{2}q-\frac{12}{19}x+\frac{12}{19}.\frac{13}{2}& \text{Uitwerken } \\ & =qx-\frac{13}{2}q-\frac{12}{19}x+\frac{156}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{13}{2}q-\frac{12}{19}x+\frac{78}{19} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{2}-x)(\frac{-7}{2}-q)& =(\color{red}{-x}+\color{orange}{\frac{-15}{2}}).(\color{green}{-q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{2}x+\frac{15}{2}q+\frac{15}{2}.\frac{7}{2}& \text{Uitwerken } \\ & =qx+\frac{7}{2}x+\frac{15}{2}q+\frac{105}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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