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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-18}{6}+x)(\frac{-15}{8}+b)& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{15}{8}x-3b+3.\frac{15}{8}& \text{Uitwerken } \\ & =bx-\frac{15}{8}x-3b+\frac{45}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{15}{3})((-17)-a)& =(\color{red}{b}+\color{orange}{5}).(\color{green}{-a}+\color{blue}{(-17)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-17)} + \color{orange}{(5)} . \color{green}{(-a)} + \color{orange}{(5)} . \color{blue}{(-17)}& \text{Boogjes en uitschrijven} \\ & = -ab-17b-5a-5.17& \text{Uitwerken } \\ & =-ab-17b-5a-85 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-12}{10})(x-\frac{-17}{9})& =(\color{red}{a}+\color{orange}{\frac{-6}{5}}).(\color{green}{x}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{9}a-\frac{6}{5}x-\frac{6}{5}.\frac{17}{9}& \text{Uitwerken } \\ & =ax+\frac{17}{9}a-\frac{6}{5}x-\frac{102}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{17}{9}a-\frac{6}{5}x-\frac{34}{15} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b+\frac{16}{9})(\frac{5}{14}+p)& =(\color{red}{b}+\color{orange}{\frac{16}{9}}).(\color{green}{p}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{16}{9})} . \color{green}{(p)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{14}b+\frac{16}{9}p+\frac{16}{9}.\frac{5}{14}& \text{Uitwerken } \\ & =bp+\frac{5}{14}b+\frac{16}{9}p+\frac{80}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{14}b+\frac{16}{9}p+\frac{40}{63} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{7}-a)(\frac{-6}{8}-p)& =(\color{red}{-a}+\color{orange}{\frac{4}{7}}).(\color{green}{-p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{4}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{4}a-\frac{4}{7}p-\frac{4}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =ap+\frac{3}{4}a-\frac{4}{7}p-\frac{12}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{4}a-\frac{4}{7}p-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{10}{19}-b)(q+\frac{-1}{19})& =(\color{red}{-b}+\color{orange}{\frac{10}{19}}).(\color{green}{q}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{10}{19})} . \color{green}{(q)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{19}b+\frac{10}{19}q-\frac{10}{19}.\frac{1}{19}& \text{Uitwerken } \\ & =-bq+\frac{1}{19}b+\frac{10}{19}q-\frac{10}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}((-18)-p)(p-\frac{-9}{20})& =(\color{red}{-p}+\color{orange}{(-18)}).(\color{green}{p}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(-18)} . \color{green}{(p)} + \color{orange}{(-18)} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{9}{20}p-18p-18.\frac{9}{20}& \text{Uitwerken } \\ & =-p^2+((\frac{-9}{20})+(-18))p-\frac{162}{20} & \text{Neem samen} \\ &=-p^2-\frac{369}{20}p-\frac{162}{20} & \text{Maak de som} \\ &=-p^2-\frac{369}{20}p-\frac{81}{10} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-7}{15})(\frac{-7}{7}+x)& =(\color{red}{q}+\color{orange}{\frac{7}{15}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{15})} . \color{green}{(x)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q+\frac{7}{15}x-\frac{7}{15}.1& \text{Uitwerken } \\ & =qx-1q+\frac{7}{15}x-\frac{7}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{12}{9}+a)(\frac{-13}{10}-x)& =(\color{red}{a}+\color{orange}{\frac{4}{3}}).(\color{green}{-x}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{13}{10}a-\frac{4}{3}x-\frac{4}{3}.\frac{13}{10}& \text{Uitwerken } \\ & =-ax-\frac{13}{10}a-\frac{4}{3}x-\frac{52}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{13}{10}a-\frac{4}{3}x-\frac{26}{15} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{17}{11}+p)(\frac{7}{9}+b)& =(\color{red}{p}+\color{orange}{\frac{17}{11}}).(\color{green}{b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{17}{11})} . \color{green}{(b)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{9}p+\frac{17}{11}b+\frac{17}{11}.\frac{7}{9}& \text{Uitwerken } \\ & =bp+\frac{7}{9}p+\frac{17}{11}b+\frac{119}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{8}+x)(\frac{-17}{2}-a)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-a}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(2)} . \color{green}{(-a)} + \color{orange}{(2)} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{17}{2}x-2a-2.\frac{17}{2}& \text{Uitwerken } \\ & =-ax-\frac{17}{2}x-2a-\frac{34}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{17}{2}x-2a-17 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{5}{10}+q)(b+12)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{12})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(12)} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = bq+12q+\frac{1}{2}b+\frac{1}{2}.12& \text{Uitwerken } \\ & =bq+12q+\frac{1}{2}b+\frac{12}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+12q+\frac{1}{2}b+6 & \text{Vereenvoudig} \\\end{align}\)
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