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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{19}{9})(q-\frac{-19}{16})& =(\color{red}{x}+\color{orange}{\frac{-19}{9}}).(\color{green}{q}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{16}x-\frac{19}{9}q-\frac{19}{9}.\frac{19}{16}& \text{Uitwerken } \\ & =qx+\frac{19}{16}x-\frac{19}{9}q-\frac{361}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{2}{16})(\frac{6}{2}+b)& =(\color{red}{x}+\color{orange}{\frac{-1}{8}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{-1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bx+3x-\frac{1}{8}b-\frac{1}{8}.3& \text{Uitwerken } \\ & =bx+3x-\frac{1}{8}b-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}((-2)+x)(\frac{19}{8}+p)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{19}{8}x-2p-2.\frac{19}{8}& \text{Uitwerken } \\ & =px+\frac{19}{8}x-2p-\frac{38}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{19}{8}x-2p-\frac{19}{4} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-16}{2})(b+\frac{15}{18})& =(\color{red}{q}+\color{orange}{8}).(\color{green}{b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(8)} . \color{green}{(b)} + \color{orange}{(8)} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{6}q+8b+8.\frac{5}{6}& \text{Uitwerken } \\ & =bq+\frac{5}{6}q+8b+\frac{40}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{5}{6}q+8b+\frac{20}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p+\frac{-1}{19})(a+\frac{13}{16})& =(\color{red}{p}+\color{orange}{\frac{-1}{19}}).(\color{green}{a}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{-1}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{16}p-\frac{1}{19}a-\frac{1}{19}.\frac{13}{16}& \text{Uitwerken } \\ & =ap+\frac{13}{16}p-\frac{1}{19}a-\frac{13}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-1}{13})(\frac{17}{20}+a)& =(\color{red}{a}+\color{orange}{\frac{1}{13}}).(\color{green}{a}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{1}{13})} . \color{green}{(a)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{17}{20}a+\frac{1}{13}a+\frac{1}{13}.\frac{17}{20}& \text{Uitwerken } \\ & =a^2+(\frac{17}{20}+\frac{1}{13})a+\frac{17}{260} & \text{Neem samen} \\ &=a^2+\frac{241}{260}a+\frac{17}{260} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{15}{15}+q)(\frac{12}{6}-x)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qx+2q-1x+1.2& \text{Uitwerken } \\ & =-qx+2q-1x+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-15}{8}-x)(\frac{19}{5}+p)& =(\color{red}{-x}+\color{orange}{\frac{-15}{8}}).(\color{green}{p}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{5}x-\frac{15}{8}p-\frac{15}{8}.\frac{19}{5}& \text{Uitwerken } \\ & =-px-\frac{19}{5}x-\frac{15}{8}p-\frac{285}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{19}{5}x-\frac{15}{8}p-\frac{57}{8} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{11}-p)(b+\frac{-17}{3})& =(\color{red}{-p}+\color{orange}{\frac{5}{11}}).(\color{green}{b}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{5}{11})} . \color{green}{(b)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{3}p+\frac{5}{11}b-\frac{5}{11}.\frac{17}{3}& \text{Uitwerken } \\ & =-bp+\frac{17}{3}p+\frac{5}{11}b-\frac{85}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{1}{17}-p)(p+\frac{-15}{18})& =(\color{red}{-p}+\color{orange}{\frac{1}{17}}).(\color{green}{p}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{1}{17})} . \color{green}{(p)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{5}{6}p+\frac{1}{17}p-\frac{1}{17}.\frac{5}{6}& \text{Uitwerken } \\ & =-p^2+(\frac{5}{6}+\frac{1}{17})p-\frac{5}{102} & \text{Neem samen} \\ &=-p^2+\frac{91}{102}p-\frac{5}{102} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{13}-a)(a+\frac{-20}{14})& =(\color{red}{-a}+\color{orange}{\frac{-19}{13}}).(\color{green}{a}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{10}{7}a-\frac{19}{13}a+\frac{19}{13}.\frac{10}{7}& \text{Uitwerken } \\ & =-a^2+(\frac{10}{7}+(\frac{-19}{13}))a+(\frac{-190}{91}) & \text{Neem samen} \\ &=-a^2-\frac{3}{91}a+(\frac{-190}{91}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{18}{15}-x)(p+\frac{8}{6})& =(\color{red}{-x}+\color{orange}{\frac{6}{5}}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{3}x+\frac{6}{5}p+\frac{6}{5}.\frac{4}{3}& \text{Uitwerken } \\ & =-px-\frac{4}{3}x+\frac{6}{5}p+\frac{24}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{4}{3}x+\frac{6}{5}p+\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
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