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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{2}{10})(\frac{-10}{4}-q)& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{-q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{2}x+\frac{1}{5}q+\frac{1}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =-qx-\frac{5}{2}x+\frac{1}{5}q+\frac{5}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{5}{2}x+\frac{1}{5}q+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b-\frac{13}{11})(p+\frac{-4}{16})& =(\color{red}{b}+\color{orange}{\frac{-13}{11}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{4}b-\frac{13}{11}p+\frac{13}{11}.\frac{1}{4}& \text{Uitwerken } \\ & =bp-\frac{1}{4}b-\frac{13}{11}p+\frac{13}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{2}-p)(a-\frac{-11}{6})& =(\color{red}{-p}+\color{orange}{(-9)}).(\color{green}{a}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(-9)} . \color{green}{(a)} + \color{orange}{(-9)} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{6}p-9a-9.\frac{11}{6}& \text{Uitwerken } \\ & =-ap-\frac{11}{6}p-9a-\frac{99}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{11}{6}p-9a-\frac{33}{2} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-15}{10})(\frac{7}{19}-q)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{-q}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{19}a-\frac{3}{2}q+\frac{3}{2}.\frac{7}{19}& \text{Uitwerken } \\ & =-aq+\frac{7}{19}a-\frac{3}{2}q+\frac{21}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{14}-a)(p+(-7))& =(\color{red}{-a}+\color{orange}{\frac{-3}{14}}).(\color{green}{p}+\color{blue}{(-7)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(-7)} + \color{orange}{(\frac{-3}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{14})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = -ap+7a-\frac{3}{14}p+\frac{3}{14}.7& \text{Uitwerken } \\ & =-ap+7a-\frac{3}{14}p+\frac{21}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+7a-\frac{3}{14}p+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{5}{2}+p)(b+\frac{4}{14})& =(\color{red}{p}+\color{orange}{\frac{5}{2}}).(\color{green}{b}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{7}p+\frac{5}{2}b+\frac{5}{2}.\frac{2}{7}& \text{Uitwerken } \\ & =bp+\frac{2}{7}p+\frac{5}{2}b+\frac{10}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{7}p+\frac{5}{2}b+\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-1}{20}+q)(\frac{9}{13}+q)& =(\color{red}{q}+\color{orange}{\frac{-1}{20}}).(\color{green}{q}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{-1}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{9}{13}q-\frac{1}{20}q-\frac{1}{20}.\frac{9}{13}& \text{Uitwerken } \\ & =q^2+(\frac{9}{13}+(\frac{-1}{20}))q-(\frac{-9}{260}) & \text{Neem samen} \\ &=q^2+\frac{167}{260}q-(\frac{-9}{260}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{15}{20}+q)(x-19)& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{(-19)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-19)} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = qx-19q+\frac{3}{4}x-\frac{3}{4}.19& \text{Uitwerken } \\ & =qx-19q+\frac{3}{4}x-\frac{57}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-10}{6})(b-\frac{9}{17})& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{b}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{17}p-\frac{5}{3}b+\frac{5}{3}.\frac{9}{17}& \text{Uitwerken } \\ & =bp-\frac{9}{17}p-\frac{5}{3}b+\frac{45}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{9}{17}p-\frac{5}{3}b+\frac{15}{17} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{16}{6}+a)(\frac{-1}{10}+q)& =(\color{red}{a}+\color{orange}{\frac{8}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{10}a+\frac{8}{3}q-\frac{8}{3}.\frac{1}{10}& \text{Uitwerken } \\ & =aq-\frac{1}{10}a+\frac{8}{3}q-\frac{8}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{10}a+\frac{8}{3}q-\frac{4}{15} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{5}-a)(a+\frac{-16}{20})& =(\color{red}{-a}+\color{orange}{\frac{16}{5}}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{16}{5})} . \color{green}{(a)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{4}{5}a+\frac{16}{5}a-\frac{16}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =-a^2+(\frac{4}{5}+\frac{16}{5})a-\frac{64}{25} & \text{Neem samen} \\ &=-a^2+\frac{20}{5}a-\frac{64}{25} & \text{Maak de som} \\ &=-a^2+4a-\frac{64}{25} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-7}{11})(a+\frac{15}{3})& =(\color{red}{a}+\color{orange}{\frac{-7}{11}}).(\color{green}{a}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(5)} + \color{orange}{(\frac{-7}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = aa+5a-\frac{7}{11}a-\frac{7}{11}.5& \text{Uitwerken } \\ & =a^2+(5+(\frac{-7}{11}))a-(\frac{-35}{11}) & \text{Neem samen} \\ &=a^2+\frac{48}{11}a-(\frac{-35}{11}) & \text{Maak de som} \\\end{align}\)
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