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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{14}{19}-a)(\frac{15}{4}-a)& =(\color{red}{-a}+\color{orange}{\frac{14}{19}}).(\color{green}{-a}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{14}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{15}{4}a-\frac{14}{19}a+\frac{14}{19}.\frac{15}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-15}{4})+(\frac{-14}{19}))a+\frac{210}{76} & \text{Neem samen} \\ &=a^2-\frac{341}{76}a+\frac{210}{76} & \text{Maak de som} \\ &=a^2-\frac{341}{76}a+\frac{105}{38} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-16}{3})(p-19)& =(\color{red}{p}+\color{orange}{\frac{16}{3}}).(\color{green}{p}+\color{blue}{(-19)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-19)} + \color{orange}{(\frac{16}{3})} . \color{green}{(p)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = pp-19p+\frac{16}{3}p-\frac{16}{3}.19& \text{Uitwerken } \\ & =p^2+((-19)+\frac{16}{3})p-(\frac{-304}{3}) & \text{Neem samen} \\ &=p^2-\frac{41}{3}p-(\frac{-304}{3}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(x-\frac{6}{3})(\frac{-4}{14}-x)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{-x}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(-2)} . \color{green}{(-x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{2}{7}x+2x+2.\frac{2}{7}& \text{Uitwerken } \\ & =-x^2+((\frac{-2}{7})+2)x+(\frac{-4}{7}) & \text{Neem samen} \\ &=-x^2+\frac{12}{7}x+(\frac{-4}{7}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-6}{15})(p+\frac{3}{17})& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{p}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{3}{17}p-\frac{2}{5}p-\frac{2}{5}.\frac{3}{17}& \text{Uitwerken } \\ & =p^2+(\frac{3}{17}+(\frac{-2}{5}))p-(\frac{-6}{85}) & \text{Neem samen} \\ &=p^2-\frac{19}{85}p-(\frac{-6}{85}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{6}-x)(a+20)& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{20})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(20)} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = -ax-20x-1a-1.20& \text{Uitwerken } \\ & =-ax-20x-1a-20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-4}{12})(b+\frac{-11}{16})& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{16}a-\frac{1}{3}b+\frac{1}{3}.\frac{11}{16}& \text{Uitwerken } \\ & =ab-\frac{11}{16}a-\frac{1}{3}b+\frac{11}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{16}{15})(q-\frac{-8}{20})& =(\color{red}{b}+\color{orange}{\frac{-16}{15}}).(\color{green}{q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{5}b-\frac{16}{15}q-\frac{16}{15}.\frac{2}{5}& \text{Uitwerken } \\ & =bq+\frac{2}{5}b-\frac{16}{15}q-\frac{32}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-9}{6}+p)(q+\frac{18}{8})& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{4}p-\frac{3}{2}q-\frac{3}{2}.\frac{9}{4}& \text{Uitwerken } \\ & =pq+\frac{9}{4}p-\frac{3}{2}q-\frac{27}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-7}{18})(\frac{-9}{14}-p)& =(\color{red}{x}+\color{orange}{\frac{-7}{18}}).(\color{green}{-p}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{9}{14}x+\frac{7}{18}p+\frac{7}{18}.\frac{9}{14}& \text{Uitwerken } \\ & =-px-\frac{9}{14}x+\frac{7}{18}p+\frac{63}{252} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{9}{14}x+\frac{7}{18}p+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-20}{15})(x+\frac{5}{3})& =(\color{red}{p}+\color{orange}{\frac{-4}{3}}).(\color{green}{x}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{3}p-\frac{4}{3}x-\frac{4}{3}.\frac{5}{3}& \text{Uitwerken } \\ & =px+\frac{5}{3}p-\frac{4}{3}x-\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{12}{20})(q-\frac{16}{11})& =(\color{red}{x}+\color{orange}{\frac{3}{5}}).(\color{green}{q}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{11}x+\frac{3}{5}q-\frac{3}{5}.\frac{16}{11}& \text{Uitwerken } \\ & =qx-\frac{16}{11}x+\frac{3}{5}q-\frac{48}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{6}{14}-x)((-19)+a)& =(\color{red}{-x}+\color{orange}{\frac{3}{7}}).(\color{green}{a}+\color{blue}{(-19)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(-19)} + \color{orange}{(\frac{3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = -ax+19x+\frac{3}{7}a-\frac{3}{7}.19& \text{Uitwerken } \\ & =-ax+19x+\frac{3}{7}a-\frac{57}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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