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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{14}{8}+x)(a-\frac{9}{13})& =(\color{red}{x}+\color{orange}{\frac{7}{4}}).(\color{green}{a}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{13}x+\frac{7}{4}a-\frac{7}{4}.\frac{9}{13}& \text{Uitwerken } \\ & =ax-\frac{9}{13}x+\frac{7}{4}a-\frac{63}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-13}{19}+a)(b-\frac{10}{15})& =(\color{red}{a}+\color{orange}{\frac{-13}{19}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{3}a-\frac{13}{19}b+\frac{13}{19}.\frac{2}{3}& \text{Uitwerken } \\ & =ab-\frac{2}{3}a-\frac{13}{19}b+\frac{26}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{20}{6})(\frac{-12}{19}+a)& =(\color{red}{a}+\color{orange}{\frac{10}{3}}).(\color{green}{a}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{12}{19}a+\frac{10}{3}a-\frac{10}{3}.\frac{12}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-12}{19})+\frac{10}{3})a-(\frac{-120}{57}) & \text{Neem samen} \\ &=a^2+\frac{154}{57}a-(\frac{-120}{57}) & \text{Maak de som} \\ &=a^2+\frac{154}{57}a+\frac{40}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(p+\frac{13}{9})(\frac{10}{18}-b)& =(\color{red}{p}+\color{orange}{\frac{13}{9}}).(\color{green}{-b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{13}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{9}p-\frac{13}{9}b+\frac{13}{9}.\frac{5}{9}& \text{Uitwerken } \\ & =-bp+\frac{5}{9}p-\frac{13}{9}b+\frac{65}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{8}+a)(\frac{19}{5}+x)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{5}a+\frac{1}{2}x+\frac{1}{2}.\frac{19}{5}& \text{Uitwerken } \\ & =ax+\frac{19}{5}a+\frac{1}{2}x+\frac{19}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{12}{12})(\frac{16}{6}-x)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{8}{3}x+1x-1.\frac{8}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{8}{3}+1)x-\frac{8}{3} & \text{Neem samen} \\ &=-x^2+\frac{11}{3}x-\frac{8}{3} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}((-16)+b)(a-\frac{13}{18})& =(\color{red}{b}+\color{orange}{(-16)}).(\color{green}{a}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(-16)} . \color{green}{(a)} + \color{orange}{(-16)} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{18}b-16a+16.\frac{13}{18}& \text{Uitwerken } \\ & =ab-\frac{13}{18}b-16a+\frac{208}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{13}{18}b-16a+\frac{104}{9} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-15}{17}+a)(p+\frac{-20}{18})& =(\color{red}{a}+\color{orange}{\frac{-15}{17}}).(\color{green}{p}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{9}a-\frac{15}{17}p+\frac{15}{17}.\frac{10}{9}& \text{Uitwerken } \\ & =ap-\frac{10}{9}a-\frac{15}{17}p+\frac{150}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{10}{9}a-\frac{15}{17}p+\frac{50}{51} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-4}{2})(\frac{5}{10}-p)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(2)} . \color{green}{(-p)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{2}x-2p+2.\frac{1}{2}& \text{Uitwerken } \\ & =-px+\frac{1}{2}x-2p+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{1}{2}x-2p+1 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-20}{10})(\frac{18}{15}+p)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{6}{5}x+2p+2.\frac{6}{5}& \text{Uitwerken } \\ & =px+\frac{6}{5}x+2p+\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{17}-x)(\frac{-19}{18}+p)& =(\color{red}{-x}+\color{orange}{\frac{10}{17}}).(\color{green}{p}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{10}{17})} . \color{green}{(p)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{19}{18}x+\frac{10}{17}p-\frac{10}{17}.\frac{19}{18}& \text{Uitwerken } \\ & =-px+\frac{19}{18}x+\frac{10}{17}p-\frac{190}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{19}{18}x+\frac{10}{17}p-\frac{95}{153} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p-\frac{18}{9})(b-\frac{9}{16})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{16}p-2b+2.\frac{9}{16}& \text{Uitwerken } \\ & =bp-\frac{9}{16}p-2b+\frac{18}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{9}{16}p-2b+\frac{9}{8} & \text{Vereenvoudig} \\\end{align}\)
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