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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{5}{2}-x)(\frac{13}{15}+x)& =(\color{red}{-x}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{\frac{13}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{15})} + \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{13}{15})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{13}{15}x+\frac{5}{2}x+\frac{5}{2}.\frac{13}{15}& \text{Uitwerken } \\ & =-x^2+((\frac{-13}{15})+\frac{5}{2})x+(\frac{-65}{30}) & \text{Neem samen} \\ &=-x^2+\frac{49}{30}x+(\frac{-65}{30}) & \text{Maak de som} \\ &=-x^2+\frac{49}{30}x+(\frac{-13}{6}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(b+\frac{8}{6})(a-\frac{-9}{5})& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{5}b+\frac{4}{3}a+\frac{4}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =ab+\frac{9}{5}b+\frac{4}{3}a+\frac{36}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{9}{5}b+\frac{4}{3}a+\frac{12}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-19}{16})(q+\frac{6}{12})& =(\color{red}{x}+\color{orange}{\frac{-19}{16}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}x-\frac{19}{16}q-\frac{19}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}x-\frac{19}{16}q-\frac{19}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+(-4))(q+\frac{-16}{4})& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aq-4a-4q+4.4& \text{Uitwerken } \\ & =aq-4a-4q+16 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-20}{20})(x+\frac{17}{20})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{20}q-1x-1.\frac{17}{20}& \text{Uitwerken } \\ & =qx+\frac{17}{20}q-1x-\frac{17}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-9}{4})(b+\frac{-20}{2})& =(\color{red}{p}+\color{orange}{\frac{9}{4}}).(\color{green}{b}+\color{blue}{(-10)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-10)} + \color{orange}{(\frac{9}{4})} . \color{green}{(b)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = bp-10p+\frac{9}{4}b-\frac{9}{4}.10& \text{Uitwerken } \\ & =bp-10p+\frac{9}{4}b-\frac{90}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-10p+\frac{9}{4}b-\frac{45}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{18}{7}+a)(\frac{6}{9}+x)& =(\color{red}{a}+\color{orange}{\frac{18}{7}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{18}{7})} . \color{green}{(x)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}a+\frac{18}{7}x+\frac{18}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}a+\frac{18}{7}x+\frac{36}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{3}a+\frac{18}{7}x+\frac{12}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-6}{13})(b-\frac{12}{9})& =(\color{red}{p}+\color{orange}{\frac{-6}{13}}).(\color{green}{b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{3}p-\frac{6}{13}b+\frac{6}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =bp-\frac{4}{3}p-\frac{6}{13}b+\frac{24}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{4}{3}p-\frac{6}{13}b+\frac{8}{13} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-20}{6}+q)(q-\frac{20}{7})& =(\color{red}{q}+\color{orange}{\frac{-10}{3}}).(\color{green}{q}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{20}{7}q-\frac{10}{3}q+\frac{10}{3}.\frac{20}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-20}{7})+(\frac{-10}{3}))q+\frac{200}{21} & \text{Neem samen} \\ &=q^2-\frac{130}{21}q+\frac{200}{21} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-5}{4})(q-\frac{8}{9})& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{9}p-\frac{5}{4}q+\frac{5}{4}.\frac{8}{9}& \text{Uitwerken } \\ & =pq-\frac{8}{9}p-\frac{5}{4}q+\frac{40}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{8}{9}p-\frac{5}{4}q+\frac{10}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{3}{4})(q-\frac{19}{5})& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{q}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{5}x+\frac{3}{4}q-\frac{3}{4}.\frac{19}{5}& \text{Uitwerken } \\ & =qx-\frac{19}{5}x+\frac{3}{4}q-\frac{57}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{2}{15})(p-\frac{-18}{13})& =(\color{red}{b}+\color{orange}{\frac{2}{15}}).(\color{green}{p}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{2}{15})} . \color{green}{(p)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{18}{13}b+\frac{2}{15}p+\frac{2}{15}.\frac{18}{13}& \text{Uitwerken } \\ & =bp+\frac{18}{13}b+\frac{2}{15}p+\frac{36}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{18}{13}b+\frac{2}{15}p+\frac{12}{65} & \text{Vereenvoudig} \\\end{align}\)
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