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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{1}{17})(\frac{18}{16}-p)& =(\color{red}{a}+\color{orange}{\frac{-1}{17}}).(\color{green}{-p}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{8}a+\frac{1}{17}p-\frac{1}{17}.\frac{9}{8}& \text{Uitwerken } \\ & =-ap+\frac{9}{8}a+\frac{1}{17}p-\frac{9}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-6}{3})(b-9)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{(-9)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-9)} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = bb-9b-2b+2.9& \text{Uitwerken } \\ & =b^2+((-9)+(-2))b+18 & \text{Neem samen} \\ &=b^2-11b+18 & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(x-\frac{13}{15})(p+\frac{-4}{16})& =(\color{red}{x}+\color{orange}{\frac{-13}{15}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{4}x-\frac{13}{15}p+\frac{13}{15}.\frac{1}{4}& \text{Uitwerken } \\ & =px-\frac{1}{4}x-\frac{13}{15}p+\frac{13}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-13}{7})(a+\frac{-14}{5})& =(\color{red}{x}+\color{orange}{\frac{-13}{7}}).(\color{green}{a}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{14}{5}x-\frac{13}{7}a+\frac{13}{7}.\frac{14}{5}& \text{Uitwerken } \\ & =ax-\frac{14}{5}x-\frac{13}{7}a+\frac{182}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{14}{5}x-\frac{13}{7}a+\frac{26}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-12}{17})(a-\frac{19}{9})& =(\color{red}{p}+\color{orange}{\frac{12}{17}}).(\color{green}{a}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{9}p+\frac{12}{17}a-\frac{12}{17}.\frac{19}{9}& \text{Uitwerken } \\ & =ap-\frac{19}{9}p+\frac{12}{17}a-\frac{228}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{19}{9}p+\frac{12}{17}a-\frac{76}{51} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-5}{18})(p+\frac{11}{8})& =(\color{red}{a}+\color{orange}{\frac{-5}{18}}).(\color{green}{p}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{8}a-\frac{5}{18}p-\frac{5}{18}.\frac{11}{8}& \text{Uitwerken } \\ & =ap+\frac{11}{8}a-\frac{5}{18}p-\frac{55}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{18}{4}-b)(\frac{6}{13}+x)& =(\color{red}{-b}+\color{orange}{\frac{9}{2}}).(\color{green}{x}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{6}{13}b+\frac{9}{2}x+\frac{9}{2}.\frac{6}{13}& \text{Uitwerken } \\ & =-bx-\frac{6}{13}b+\frac{9}{2}x+\frac{54}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{6}{13}b+\frac{9}{2}x+\frac{27}{13} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{1}{18}+p)(x-\frac{-10}{14})& =(\color{red}{p}+\color{orange}{\frac{1}{18}}).(\color{green}{x}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{1}{18})} . \color{green}{(x)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{7}p+\frac{1}{18}x+\frac{1}{18}.\frac{5}{7}& \text{Uitwerken } \\ & =px+\frac{5}{7}p+\frac{1}{18}x+\frac{5}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-3}{11}-a)(\frac{12}{11}+a)& =(\color{red}{-a}+\color{orange}{\frac{-3}{11}}).(\color{green}{a}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{12}{11}a-\frac{3}{11}a-\frac{3}{11}.\frac{12}{11}& \text{Uitwerken } \\ & =-a^2+((\frac{-12}{11})+(\frac{-3}{11}))a-\frac{36}{121} & \text{Neem samen} \\ &=-a^2-\frac{15}{11}a-\frac{36}{121} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(b-6)(\frac{13}{11}+p)& =(\color{red}{b}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{11}b-6p-6.\frac{13}{11}& \text{Uitwerken } \\ & =bp+\frac{13}{11}b-6p-\frac{78}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-10}{19})(x-\frac{-13}{8})& =(\color{red}{q}+\color{orange}{\frac{10}{19}}).(\color{green}{x}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{10}{19})} . \color{green}{(x)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{8}q+\frac{10}{19}x+\frac{10}{19}.\frac{13}{8}& \text{Uitwerken } \\ & =qx+\frac{13}{8}q+\frac{10}{19}x+\frac{130}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{13}{8}q+\frac{10}{19}x+\frac{65}{76} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{2}{8}+x)(b+\frac{-20}{10})& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bx-2x+\frac{1}{4}b-\frac{1}{4}.2& \text{Uitwerken } \\ & =bx-2x+\frac{1}{4}b-\frac{2}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-2x+\frac{1}{4}b-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
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