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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-13}{15})(6-b)& =(\color{red}{b}+\color{orange}{\frac{13}{15}}).(\color{green}{-b}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(6)} + \color{orange}{(\frac{13}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -bb+6b-\frac{13}{15}b+\frac{13}{15}.6& \text{Uitwerken } \\ & =-b^2+(6+(\frac{-13}{15}))b+(\frac{-78}{15}) & \text{Neem samen} \\ &=-b^2+\frac{77}{15}b+(\frac{-78}{15}) & \text{Maak de som} \\ &=-b^2+\frac{77}{15}b+(\frac{-26}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-13}{7})(p-\frac{-1}{19})& =(\color{red}{q}+\color{orange}{\frac{13}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{13}{7})} . \color{green}{(p)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{19}q+\frac{13}{7}p+\frac{13}{7}.\frac{1}{19}& \text{Uitwerken } \\ & =pq+\frac{1}{19}q+\frac{13}{7}p+\frac{13}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-2}{13}+q)(\frac{-17}{2}+p)& =(\color{red}{q}+\color{orange}{\frac{-2}{13}}).(\color{green}{p}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{2}q-\frac{2}{13}p+\frac{2}{13}.\frac{17}{2}& \text{Uitwerken } \\ & =pq-\frac{17}{2}q-\frac{2}{13}p+\frac{34}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{17}{2}q-\frac{2}{13}p+\frac{17}{13} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{12}-b)(\frac{-2}{2}+b)& =(\color{red}{-b}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bb+1b+\frac{4}{3}b-\frac{4}{3}.1& \text{Uitwerken } \\ & =-b^2+(1+\frac{4}{3})b-\frac{4}{3} & \text{Neem samen} \\ &=-b^2+\frac{7}{3}b-\frac{4}{3} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(p+\frac{-14}{5})(q-\frac{19}{2})& =(\color{red}{p}+\color{orange}{\frac{-14}{5}}).(\color{green}{q}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{2}p-\frac{14}{5}q+\frac{14}{5}.\frac{19}{2}& \text{Uitwerken } \\ & =pq-\frac{19}{2}p-\frac{14}{5}q+\frac{266}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{19}{2}p-\frac{14}{5}q+\frac{133}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{4}{15}-b)(\frac{-13}{5}-b)& =(\color{red}{-b}+\color{orange}{\frac{4}{15}}).(\color{green}{-b}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{4}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{13}{5}b-\frac{4}{15}b-\frac{4}{15}.\frac{13}{5}& \text{Uitwerken } \\ & =b^2+(\frac{13}{5}+(\frac{-4}{15}))b-(\frac{-52}{75}) & \text{Neem samen} \\ &=b^2+\frac{35}{15}b-(\frac{-52}{75}) & \text{Maak de som} \\ &=b^2+\frac{7}{3}b+\frac{52}{75} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(5-p)(x-\frac{18}{18})& =(\color{red}{-p}+\color{orange}{5}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -px+1p+5x-5.1& \text{Uitwerken } \\ & =-px+1p+5x-5 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-9}{15})((-9)+a)& =(\color{red}{a}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-9)} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = aa-9a+\frac{3}{5}a-\frac{3}{5}.9& \text{Uitwerken } \\ & =a^2+((-9)+\frac{3}{5})a-(\frac{-27}{5}) & \text{Neem samen} \\ &=a^2-\frac{42}{5}a-(\frac{-27}{5}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{13}+b)(a+\frac{-2}{12})& =(\color{red}{b}+\color{orange}{\frac{5}{13}}).(\color{green}{a}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{5}{13})} . \color{green}{(a)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{6}b+\frac{5}{13}a-\frac{5}{13}.\frac{1}{6}& \text{Uitwerken } \\ & =ab-\frac{1}{6}b+\frac{5}{13}a-\frac{5}{78} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-8}{2}-q)(\frac{10}{15}+x)& =(\color{red}{-q}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{3}q-4x-4.\frac{2}{3}& \text{Uitwerken } \\ & =-qx-\frac{2}{3}q-4x-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-20}{16}-b)(b-\frac{-5}{3})& =(\color{red}{-b}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{5}{3}b-\frac{5}{4}b-\frac{5}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-5}{3})+(\frac{-5}{4}))b-\frac{25}{12} & \text{Neem samen} \\ &=-b^2-\frac{35}{12}b-\frac{25}{12} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{4}{8}-b)(\frac{5}{16}-b)& =(\color{red}{-b}+\color{orange}{\frac{1}{2}}).(\color{green}{-b}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{5}{16}b-\frac{1}{2}b+\frac{1}{2}.\frac{5}{16}& \text{Uitwerken } \\ & =b^2+((\frac{-5}{16})+(\frac{-1}{2}))b+\frac{5}{32} & \text{Neem samen} \\ &=b^2-\frac{13}{16}b+\frac{5}{32} & \text{Maak de som} \\\end{align}\)
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