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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-4}{11})(x+\frac{8}{2})& =(\color{red}{p}+\color{orange}{\frac{4}{11}}).(\color{green}{x}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = px+4p+\frac{4}{11}x+\frac{4}{11}.4& \text{Uitwerken } \\ & =px+4p+\frac{4}{11}x+\frac{16}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-(-16))(\frac{-15}{11}+b)& =(\color{red}{p}+\color{orange}{16}).(\color{green}{b}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(16)} . \color{green}{(b)} + \color{orange}{(16)} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{15}{11}p+16b-16.\frac{15}{11}& \text{Uitwerken } \\ & =bp-\frac{15}{11}p+16b-\frac{240}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-4}{5})(q-\frac{-13}{5})& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{13}{5}p-\frac{4}{5}q-\frac{4}{5}.\frac{13}{5}& \text{Uitwerken } \\ & =pq+\frac{13}{5}p-\frac{4}{5}q-\frac{52}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{15}{9})(\frac{12}{10}-a)& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{-a}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{6}{5}p-\frac{5}{3}a+\frac{5}{3}.\frac{6}{5}& \text{Uitwerken } \\ & =-ap+\frac{6}{5}p-\frac{5}{3}a+\frac{30}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{6}{5}p-\frac{5}{3}a+2 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{6}+p)(a+\frac{-6}{7})& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{6}{7}p+\frac{5}{3}a-\frac{5}{3}.\frac{6}{7}& \text{Uitwerken } \\ & =ap-\frac{6}{7}p+\frac{5}{3}a-\frac{30}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{6}{7}p+\frac{5}{3}a-\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{16}-q)(b-\frac{-2}{18})& =(\color{red}{-q}+\color{orange}{\frac{-7}{16}}).(\color{green}{b}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{9}q-\frac{7}{16}b-\frac{7}{16}.\frac{1}{9}& \text{Uitwerken } \\ & =-bq-\frac{1}{9}q-\frac{7}{16}b-\frac{7}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{17}{14}-a)(a+\frac{-18}{6})& =(\color{red}{-a}+\color{orange}{\frac{17}{14}}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(-3)} + \color{orange}{(\frac{17}{14})} . \color{green}{(a)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -aa+3a+\frac{17}{14}a-\frac{17}{14}.3& \text{Uitwerken } \\ & =-a^2+(3+\frac{17}{14})a-\frac{51}{14} & \text{Neem samen} \\ &=-a^2+\frac{59}{14}a-\frac{51}{14} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-11}{17}-x)(\frac{16}{3}-a)& =(\color{red}{-x}+\color{orange}{\frac{-11}{17}}).(\color{green}{-a}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{-11}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{16}{3}x+\frac{11}{17}a-\frac{11}{17}.\frac{16}{3}& \text{Uitwerken } \\ & =ax-\frac{16}{3}x+\frac{11}{17}a-\frac{176}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{13}{20})(\frac{19}{6}-p)& =(\color{red}{p}+\color{orange}{\frac{13}{20}}).(\color{green}{-p}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{13}{20})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{19}{6}p-\frac{13}{20}p+\frac{13}{20}.\frac{19}{6}& \text{Uitwerken } \\ & =-p^2+(\frac{19}{6}+(\frac{-13}{20}))p+(\frac{-247}{120}) & \text{Neem samen} \\ &=-p^2+\frac{151}{60}p+(\frac{-247}{120}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(a-\frac{19}{16})(\frac{18}{9}-a)& =(\color{red}{a}+\color{orange}{\frac{-19}{16}}).(\color{green}{-a}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-19}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -aa+2a+\frac{19}{16}a-\frac{19}{16}.2& \text{Uitwerken } \\ & =-a^2+(2+\frac{19}{16})a-\frac{38}{16} & \text{Neem samen} \\ &=-a^2+\frac{51}{16}a-\frac{38}{16} & \text{Maak de som} \\ &=-a^2+\frac{51}{16}a-\frac{19}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(p+\frac{13}{2})(\frac{16}{5}-a)& =(\color{red}{p}+\color{orange}{\frac{13}{2}}).(\color{green}{-a}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{13}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{16}{5}p-\frac{13}{2}a+\frac{13}{2}.\frac{16}{5}& \text{Uitwerken } \\ & =-ap+\frac{16}{5}p-\frac{13}{2}a+\frac{208}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{16}{5}p-\frac{13}{2}a+\frac{104}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{17}{20}-x)(\frac{7}{5}-x)& =(\color{red}{-x}+\color{orange}{\frac{17}{20}}).(\color{green}{-x}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{17}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{7}{5}x-\frac{17}{20}x+\frac{17}{20}.\frac{7}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-7}{5})+(\frac{-17}{20}))x+\frac{119}{100} & \text{Neem samen} \\ &=x^2-\frac{45}{20}x+\frac{119}{100} & \text{Maak de som} \\ &=x^2-\frac{9}{4}x+\frac{119}{100} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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