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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{10}-b)(a-\frac{12}{8})& =(\color{red}{-b}+\color{orange}{\frac{-13}{10}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{2}b-\frac{13}{10}a+\frac{13}{10}.\frac{3}{2}& \text{Uitwerken } \\ & =-ab+\frac{3}{2}b-\frac{13}{10}a+\frac{39}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-2}{5}+b)(\frac{-5}{6}-a)& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{-a}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{5}{6}b+\frac{2}{5}a+\frac{2}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =-ab-\frac{5}{6}b+\frac{2}{5}a+\frac{10}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{5}{6}b+\frac{2}{5}a+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{4}{9}-q)(\frac{11}{12}+q)& =(\color{red}{-q}+\color{orange}{\frac{4}{9}}).(\color{green}{q}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{11}{12}q+\frac{4}{9}q+\frac{4}{9}.\frac{11}{12}& \text{Uitwerken } \\ & =-q^2+((\frac{-11}{12})+\frac{4}{9})q+(\frac{-44}{108}) & \text{Neem samen} \\ &=-q^2-\frac{17}{36}q+(\frac{-44}{108}) & \text{Maak de som} \\ &=-q^2-\frac{17}{36}q+(\frac{-11}{27}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{2}{19}+q)(p+\frac{-16}{17})& =(\color{red}{q}+\color{orange}{\frac{2}{19}}).(\color{green}{p}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{2}{19})} . \color{green}{(p)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{16}{17}q+\frac{2}{19}p-\frac{2}{19}.\frac{16}{17}& \text{Uitwerken } \\ & =pq-\frac{16}{17}q+\frac{2}{19}p-\frac{32}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-13}{17})(x+\frac{9}{6})& =(\color{red}{q}+\color{orange}{\frac{-13}{17}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{2}q-\frac{13}{17}x-\frac{13}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =qx+\frac{3}{2}q-\frac{13}{17}x-\frac{39}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-20)(\frac{-11}{4}-b)& =(\color{red}{p}+\color{orange}{(-20)}).(\color{green}{-b}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(-20)} . \color{green}{(-b)} + \color{orange}{(-20)} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{11}{4}p+20b+20.\frac{11}{4}& \text{Uitwerken } \\ & =-bp-\frac{11}{4}p+20b+\frac{220}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{11}{4}p+20b+55 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-5}{13})(x-\frac{15}{2})& =(\color{red}{a}+\color{orange}{\frac{5}{13}}).(\color{green}{x}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{5}{13})} . \color{green}{(x)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{15}{2}a+\frac{5}{13}x-\frac{5}{13}.\frac{15}{2}& \text{Uitwerken } \\ & =ax-\frac{15}{2}a+\frac{5}{13}x-\frac{75}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{13}{17})(p+\frac{7}{7})& =(\color{red}{x}+\color{orange}{\frac{-13}{17}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-13}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1x-\frac{13}{17}p-\frac{13}{17}.1& \text{Uitwerken } \\ & =px+1x-\frac{13}{17}p-\frac{13}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{7}+b)(\frac{-17}{6}-a)& =(\color{red}{b}+\color{orange}{\frac{4}{7}}).(\color{green}{-a}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{4}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{17}{6}b-\frac{4}{7}a-\frac{4}{7}.\frac{17}{6}& \text{Uitwerken } \\ & =-ab-\frac{17}{6}b-\frac{4}{7}a-\frac{68}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{17}{6}b-\frac{4}{7}a-\frac{34}{21} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-3)(\frac{3}{5}+b)& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{5}q-3b-3.\frac{3}{5}& \text{Uitwerken } \\ & =bq+\frac{3}{5}q-3b-\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{15}{16}+a)(\frac{-14}{18}+q)& =(\color{red}{a}+\color{orange}{\frac{15}{16}}).(\color{green}{q}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{15}{16})} . \color{green}{(q)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{9}a+\frac{15}{16}q-\frac{15}{16}.\frac{7}{9}& \text{Uitwerken } \\ & =aq-\frac{7}{9}a+\frac{15}{16}q-\frac{105}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{7}{9}a+\frac{15}{16}q-\frac{35}{48} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x-\frac{12}{4})(\frac{15}{10}-p)& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{-p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(-3)} . \color{green}{(-p)} + \color{orange}{(-3)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{2}x+3p-3.\frac{3}{2}& \text{Uitwerken } \\ & =-px+\frac{3}{2}x+3p-\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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