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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{8}{16})(\frac{8}{10}-q)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{4}{5}q+\frac{1}{2}q-\frac{1}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =-q^2+(\frac{4}{5}+\frac{1}{2})q-\frac{4}{10} & \text{Neem samen} \\ &=-q^2+\frac{13}{10}q-\frac{4}{10} & \text{Maak de som} \\ &=-q^2+\frac{13}{10}q-\frac{2}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{14}+q)(\frac{-8}{6}-a)& =(\color{red}{q}+\color{orange}{\frac{-6}{7}}).(\color{green}{-a}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{4}{3}q+\frac{6}{7}a+\frac{6}{7}.\frac{4}{3}& \text{Uitwerken } \\ & =-aq-\frac{4}{3}q+\frac{6}{7}a+\frac{24}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{4}{3}q+\frac{6}{7}a+\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-12}{3}-p)(x-\frac{-10}{2})& =(\color{red}{-p}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(5)} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -px-5p-4x-4.5& \text{Uitwerken } \\ & =-px-5p-4x-20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-13}{14}-p)(\frac{16}{15}-b)& =(\color{red}{-p}+\color{orange}{\frac{-13}{14}}).(\color{green}{-b}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{16}{15}p+\frac{13}{14}b-\frac{13}{14}.\frac{16}{15}& \text{Uitwerken } \\ & =bp-\frac{16}{15}p+\frac{13}{14}b-\frac{208}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{16}{15}p+\frac{13}{14}b-\frac{104}{105} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{3}+a)(\frac{9}{8}+q)& =(\color{red}{a}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{8}a+3q+3.\frac{9}{8}& \text{Uitwerken } \\ & =aq+\frac{9}{8}a+3q+\frac{27}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{3}{2}-a)(b-\frac{-16}{20})& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{5}a+\frac{3}{2}b+\frac{3}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =-ab-\frac{4}{5}a+\frac{3}{2}b+\frac{12}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{4}{5}a+\frac{3}{2}b+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-6}{17})(x+\frac{18}{16})& =(\color{red}{a}+\color{orange}{\frac{6}{17}}).(\color{green}{x}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{6}{17})} . \color{green}{(x)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{8}a+\frac{6}{17}x+\frac{6}{17}.\frac{9}{8}& \text{Uitwerken } \\ & =ax+\frac{9}{8}a+\frac{6}{17}x+\frac{54}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{9}{8}a+\frac{6}{17}x+\frac{27}{68} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{4}-x)(\frac{8}{16}-x)& =(\color{red}{-x}+\color{orange}{3}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(3)} . \color{green}{(-x)} + \color{orange}{(3)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{2}x-3x+3.\frac{1}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{2})+(-3))x+\frac{3}{2} & \text{Neem samen} \\ &=x^2-\frac{7}{2}x+\frac{3}{2} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(p+(-16))(p+\frac{-17}{8})& =(\color{red}{p}+\color{orange}{(-16)}).(\color{green}{p}+\color{blue}{\frac{-17}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{8})} + \color{orange}{(-16)} . \color{green}{(p)} + \color{orange}{(-16)} . \color{blue}{(\frac{-17}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{8}p-16p+16.\frac{17}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{8})+(-16))p+\frac{272}{8} & \text{Neem samen} \\ &=p^2-\frac{145}{8}p+\frac{272}{8} & \text{Maak de som} \\ &=p^2-\frac{145}{8}p+34 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-12}{13})(\frac{13}{4}-q)& =(\color{red}{q}+\color{orange}{\frac{-12}{13}}).(\color{green}{-q}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{13}{4}q+\frac{12}{13}q-\frac{12}{13}.\frac{13}{4}& \text{Uitwerken } \\ & =-q^2+(\frac{13}{4}+\frac{12}{13})q-\frac{156}{52} & \text{Neem samen} \\ &=-q^2+\frac{217}{52}q-\frac{156}{52} & \text{Maak de som} \\ &=-q^2+\frac{217}{52}q-3 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(b-\frac{3}{5})(\frac{-20}{13}+b)& =(\color{red}{b}+\color{orange}{\frac{-3}{5}}).(\color{green}{b}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{20}{13}b-\frac{3}{5}b+\frac{3}{5}.\frac{20}{13}& \text{Uitwerken } \\ & =b^2+((\frac{-20}{13})+(\frac{-3}{5}))b+\frac{60}{65} & \text{Neem samen} \\ &=b^2-\frac{139}{65}b+\frac{60}{65} & \text{Maak de som} \\ &=b^2-\frac{139}{65}b+\frac{12}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(b+\frac{17}{13})(q-\frac{-3}{19})& =(\color{red}{b}+\color{orange}{\frac{17}{13}}).(\color{green}{q}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{17}{13})} . \color{green}{(q)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{19}b+\frac{17}{13}q+\frac{17}{13}.\frac{3}{19}& \text{Uitwerken } \\ & =bq+\frac{3}{19}b+\frac{17}{13}q+\frac{51}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-02 12:22:39