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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{20}{14})(x+\frac{-1}{5})& =(\color{red}{q}+\color{orange}{\frac{10}{7}}).(\color{green}{x}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{5}q+\frac{10}{7}x-\frac{10}{7}.\frac{1}{5}& \text{Uitwerken } \\ & =qx-\frac{1}{5}q+\frac{10}{7}x-\frac{10}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{5}q+\frac{10}{7}x-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-10}{11})(a-\frac{9}{14})& =(\color{red}{b}+\color{orange}{\frac{10}{11}}).(\color{green}{a}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{10}{11})} . \color{green}{(a)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{14}b+\frac{10}{11}a-\frac{10}{11}.\frac{9}{14}& \text{Uitwerken } \\ & =ab-\frac{9}{14}b+\frac{10}{11}a-\frac{90}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{9}{14}b+\frac{10}{11}a-\frac{45}{77} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-15}{2})(\frac{-15}{5}+x)& =(\color{red}{b}+\color{orange}{\frac{-15}{2}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{-15}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bx-3b-\frac{15}{2}x+\frac{15}{2}.3& \text{Uitwerken } \\ & =bx-3b-\frac{15}{2}x+\frac{45}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-17}{3}-q)(x+\frac{-9}{17})& =(\color{red}{-q}+\color{orange}{\frac{-17}{3}}).(\color{green}{x}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{9}{17}q-\frac{17}{3}x+\frac{17}{3}.\frac{9}{17}& \text{Uitwerken } \\ & =-qx+\frac{9}{17}q-\frac{17}{3}x+\frac{153}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{9}{17}q-\frac{17}{3}x+3 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{12}{7})(b-\frac{19}{20})& =(\color{red}{a}+\color{orange}{\frac{-12}{7}}).(\color{green}{b}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{-12}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-12}{7})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{20}a-\frac{12}{7}b+\frac{12}{7}.\frac{19}{20}& \text{Uitwerken } \\ & =ab-\frac{19}{20}a-\frac{12}{7}b+\frac{228}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{19}{20}a-\frac{12}{7}b+\frac{57}{35} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-9}{6})(\frac{16}{13}+q)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{16}{13}a+\frac{3}{2}q+\frac{3}{2}.\frac{16}{13}& \text{Uitwerken } \\ & =aq+\frac{16}{13}a+\frac{3}{2}q+\frac{48}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{16}{13}a+\frac{3}{2}q+\frac{24}{13} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-8}{15})(\frac{-19}{6}+p)& =(\color{red}{q}+\color{orange}{\frac{-8}{15}}).(\color{green}{p}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{6}q-\frac{8}{15}p+\frac{8}{15}.\frac{19}{6}& \text{Uitwerken } \\ & =pq-\frac{19}{6}q-\frac{8}{15}p+\frac{152}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{19}{6}q-\frac{8}{15}p+\frac{76}{45} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-18}{7})(\frac{-19}{12}+x)& =(\color{red}{x}+\color{orange}{\frac{-18}{7}}).(\color{green}{x}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{19}{12}x-\frac{18}{7}x+\frac{18}{7}.\frac{19}{12}& \text{Uitwerken } \\ & =x^2+((\frac{-19}{12})+(\frac{-18}{7}))x+\frac{342}{84} & \text{Neem samen} \\ &=x^2-\frac{349}{84}x+\frac{342}{84} & \text{Maak de som} \\ &=x^2-\frac{349}{84}x+\frac{57}{14} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-13}{19}+q)(\frac{-5}{10}-q)& =(\color{red}{q}+\color{orange}{\frac{-13}{19}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{2}q+\frac{13}{19}q+\frac{13}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{2})+\frac{13}{19})q+(\frac{-13}{38}) & \text{Neem samen} \\ &=-q^2+\frac{7}{38}q+(\frac{-13}{38}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p+\frac{12}{15})(\frac{5}{2}+x)& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{2}p+\frac{4}{5}x+\frac{4}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =px+\frac{5}{2}p+\frac{4}{5}x+\frac{20}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{5}{2}p+\frac{4}{5}x+2 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{7}{14}+q)(b-\frac{14}{13})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{14}{13}q+\frac{1}{2}b-\frac{1}{2}.\frac{14}{13}& \text{Uitwerken } \\ & =bq-\frac{14}{13}q+\frac{1}{2}b-\frac{14}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{14}{13}q+\frac{1}{2}b-\frac{7}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{10}{3}+a)(p-\frac{4}{4})& =(\color{red}{a}+\color{orange}{\frac{10}{3}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a+\frac{10}{3}p-\frac{10}{3}.1& \text{Uitwerken } \\ & =ap-1a+\frac{10}{3}p-\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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