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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-10}{18})(x+\frac{8}{13})& =(\color{red}{q}+\color{orange}{\frac{-5}{9}}).(\color{green}{x}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{8}{13}q-\frac{5}{9}x-\frac{5}{9}.\frac{8}{13}& \text{Uitwerken } \\ & =qx+\frac{8}{13}q-\frac{5}{9}x-\frac{40}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-9}{18})(\frac{8}{18}-a)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{-a}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{4}{9}p+\frac{1}{2}a-\frac{1}{2}.\frac{4}{9}& \text{Uitwerken } \\ & =-ap+\frac{4}{9}p+\frac{1}{2}a-\frac{4}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{4}{9}p+\frac{1}{2}a-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{13}+b)(\frac{-9}{10}+b)& =(\color{red}{b}+\color{orange}{\frac{-7}{13}}).(\color{green}{b}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{9}{10}b-\frac{7}{13}b+\frac{7}{13}.\frac{9}{10}& \text{Uitwerken } \\ & =b^2+((\frac{-9}{10})+(\frac{-7}{13}))b+\frac{63}{130} & \text{Neem samen} \\ &=b^2-\frac{187}{130}b+\frac{63}{130} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-7}{12})(\frac{7}{10}+p)& =(\color{red}{a}+\color{orange}{\frac{7}{12}}).(\color{green}{p}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{7}{12})} . \color{green}{(p)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{10}a+\frac{7}{12}p+\frac{7}{12}.\frac{7}{10}& \text{Uitwerken } \\ & =ap+\frac{7}{10}a+\frac{7}{12}p+\frac{49}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-3}{16})(q-\frac{-20}{19})& =(\color{red}{p}+\color{orange}{\frac{3}{16}}).(\color{green}{q}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{3}{16})} . \color{green}{(q)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{20}{19}p+\frac{3}{16}q+\frac{3}{16}.\frac{20}{19}& \text{Uitwerken } \\ & =pq+\frac{20}{19}p+\frac{3}{16}q+\frac{60}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{20}{19}p+\frac{3}{16}q+\frac{15}{76} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-5}{17})(p+\frac{-9}{20})& =(\color{red}{q}+\color{orange}{\frac{-5}{17}}).(\color{green}{p}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{9}{20}q-\frac{5}{17}p+\frac{5}{17}.\frac{9}{20}& \text{Uitwerken } \\ & =pq-\frac{9}{20}q-\frac{5}{17}p+\frac{45}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{9}{20}q-\frac{5}{17}p+\frac{9}{68} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-10}{3}+p)(\frac{-6}{20}+b)& =(\color{red}{p}+\color{orange}{\frac{-10}{3}}).(\color{green}{b}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{10}p-\frac{10}{3}b+\frac{10}{3}.\frac{3}{10}& \text{Uitwerken } \\ & =bp-\frac{3}{10}p-\frac{10}{3}b+\frac{30}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{10}p-\frac{10}{3}b+1 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-13}{10})(b+\frac{16}{13})& =(\color{red}{b}+\color{orange}{\frac{-13}{10}}).(\color{green}{b}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{16}{13}b-\frac{13}{10}b-\frac{13}{10}.\frac{16}{13}& \text{Uitwerken } \\ & =b^2+(\frac{16}{13}+(\frac{-13}{10}))b-(\frac{-208}{130}) & \text{Neem samen} \\ &=b^2-\frac{9}{130}b-(\frac{-208}{130}) & \text{Maak de som} \\ &=b^2-\frac{9}{130}b+\frac{8}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{-1}{8}+x)(p-\frac{20}{14})& =(\color{red}{x}+\color{orange}{\frac{-1}{8}}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{7}x-\frac{1}{8}p+\frac{1}{8}.\frac{10}{7}& \text{Uitwerken } \\ & =px-\frac{10}{7}x-\frac{1}{8}p+\frac{10}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{10}{7}x-\frac{1}{8}p+\frac{5}{28} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{10}-a)(x-\frac{13}{6})& =(\color{red}{-a}+\color{orange}{\frac{9}{5}}).(\color{green}{x}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{9}{5})} . \color{green}{(x)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{6}a+\frac{9}{5}x-\frac{9}{5}.\frac{13}{6}& \text{Uitwerken } \\ & =-ax+\frac{13}{6}a+\frac{9}{5}x-\frac{117}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{13}{6}a+\frac{9}{5}x-\frac{39}{10} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a+\frac{7}{17})(\frac{16}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{7}{17}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{7}{17})} . \color{green}{(p)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ap+4a+\frac{7}{17}p+\frac{7}{17}.4& \text{Uitwerken } \\ & =ap+4a+\frac{7}{17}p+\frac{28}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-12}{2}+x)(a-\frac{-16}{14})& =(\color{red}{x}+\color{orange}{(-6)}).(\color{green}{a}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(-6)} . \color{green}{(a)} + \color{orange}{(-6)} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{7}x-6a-6.\frac{8}{7}& \text{Uitwerken } \\ & =ax+\frac{8}{7}x-6a-\frac{48}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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