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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-17}{2})(x+\frac{-10}{13})& =(\color{red}{p}+\color{orange}{\frac{-17}{2}}).(\color{green}{x}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{-17}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{2})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{13}p-\frac{17}{2}x+\frac{17}{2}.\frac{10}{13}& \text{Uitwerken } \\ & =px-\frac{10}{13}p-\frac{17}{2}x+\frac{170}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{10}{13}p-\frac{17}{2}x+\frac{85}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{5}{6}+p)(p-\frac{13}{15})& =(\color{red}{p}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{15}p+\frac{5}{6}p-\frac{5}{6}.\frac{13}{15}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{15})+\frac{5}{6})p-(\frac{-65}{90}) & \text{Neem samen} \\ &=p^2-\frac{1}{30}p-(\frac{-65}{90}) & \text{Maak de som} \\ &=p^2-\frac{1}{30}p+\frac{13}{18} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{-6}{10}-a)(b+\frac{-1}{16})& =(\color{red}{-a}+\color{orange}{\frac{-3}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{16}a-\frac{3}{5}b+\frac{3}{5}.\frac{1}{16}& \text{Uitwerken } \\ & =-ab+\frac{1}{16}a-\frac{3}{5}b+\frac{3}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{15}{13}-x)(x-\frac{11}{19})& =(\color{red}{-x}+\color{orange}{\frac{15}{13}}).(\color{green}{x}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{15}{13})} . \color{green}{(x)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{11}{19}x+\frac{15}{13}x-\frac{15}{13}.\frac{11}{19}& \text{Uitwerken } \\ & =-x^2+(\frac{11}{19}+\frac{15}{13})x-\frac{165}{247} & \text{Neem samen} \\ &=-x^2+\frac{428}{247}x-\frac{165}{247} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-12}{19}-a)(\frac{18}{7}-q)& =(\color{red}{-a}+\color{orange}{\frac{-12}{19}}).(\color{green}{-q}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{18}{7}a+\frac{12}{19}q-\frac{12}{19}.\frac{18}{7}& \text{Uitwerken } \\ & =aq-\frac{18}{7}a+\frac{12}{19}q-\frac{216}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{18}{14}+p)(\frac{-13}{4}+b)& =(\color{red}{p}+\color{orange}{\frac{9}{7}}).(\color{green}{b}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{4}p+\frac{9}{7}b-\frac{9}{7}.\frac{13}{4}& \text{Uitwerken } \\ & =bp-\frac{13}{4}p+\frac{9}{7}b-\frac{117}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{16}{14}+b)(p+\frac{-16}{2})& =(\color{red}{b}+\color{orange}{\frac{8}{7}}).(\color{green}{p}+\color{blue}{(-8)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-8)} + \color{orange}{(\frac{8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = bp-8b+\frac{8}{7}p-\frac{8}{7}.8& \text{Uitwerken } \\ & =bp-8b+\frac{8}{7}p-\frac{64}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-1}{13}+a)(x-\frac{-5}{7})& =(\color{red}{a}+\color{orange}{\frac{-1}{13}}).(\color{green}{x}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{7}a-\frac{1}{13}x-\frac{1}{13}.\frac{5}{7}& \text{Uitwerken } \\ & =ax+\frac{5}{7}a-\frac{1}{13}x-\frac{5}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{10}{12}-q)(\frac{17}{19}-a)& =(\color{red}{-q}+\color{orange}{\frac{5}{6}}).(\color{green}{-a}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{19}q-\frac{5}{6}a+\frac{5}{6}.\frac{17}{19}& \text{Uitwerken } \\ & =aq-\frac{17}{19}q-\frac{5}{6}a+\frac{85}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{10}{18})(\frac{-20}{18}+x)& =(\color{red}{p}+\color{orange}{\frac{5}{9}}).(\color{green}{x}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{5}{9})} . \color{green}{(x)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{9}p+\frac{5}{9}x-\frac{5}{9}.\frac{10}{9}& \text{Uitwerken } \\ & =px-\frac{10}{9}p+\frac{5}{9}x-\frac{50}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-20}{10}-p)(\frac{16}{12}-p)& =(\color{red}{-p}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{3}p+2p-2.\frac{4}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{3})+2)p-(\frac{-8}{3}) & \text{Neem samen} \\ &=p^2+\frac{2}{3}p-(\frac{-8}{3}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{18}{2}-q)(\frac{10}{6}-a)& =(\color{red}{-q}+\color{orange}{9}).(\color{green}{-a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(9)} . \color{green}{(-a)} + \color{orange}{(9)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{3}q-9a+9.\frac{5}{3}& \text{Uitwerken } \\ & =aq-\frac{5}{3}q-9a+\frac{45}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{5}{3}q-9a+15 & \text{Vereenvoudig} \\\end{align}\)
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