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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-3}{7})(\frac{-6}{2}+a)& =(\color{red}{b}+\color{orange}{\frac{3}{7}}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ab-3b+\frac{3}{7}a-\frac{3}{7}.3& \text{Uitwerken } \\ & =ab-3b+\frac{3}{7}a-\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{20}+b)(\frac{14}{5}+q)& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{q}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{14}{5}b+\frac{3}{5}q+\frac{3}{5}.\frac{14}{5}& \text{Uitwerken } \\ & =bq+\frac{14}{5}b+\frac{3}{5}q+\frac{42}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-20}{8}-a)(a-\frac{-8}{9})& =(\color{red}{-a}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{8}{9}a-\frac{5}{2}a-\frac{5}{2}.\frac{8}{9}& \text{Uitwerken } \\ & =-a^2+((\frac{-8}{9})+(\frac{-5}{2}))a-\frac{40}{18} & \text{Neem samen} \\ &=-a^2-\frac{61}{18}a-\frac{40}{18} & \text{Maak de som} \\ &=-a^2-\frac{61}{18}a-\frac{20}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(x+\frac{4}{14})(\frac{12}{2}+b)& =(\color{red}{x}+\color{orange}{\frac{2}{7}}).(\color{green}{b}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(6)} + \color{orange}{(\frac{2}{7})} . \color{green}{(b)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bx+6x+\frac{2}{7}b+\frac{2}{7}.6& \text{Uitwerken } \\ & =bx+6x+\frac{2}{7}b+\frac{12}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-1}{7})(\frac{3}{17}-b)& =(\color{red}{x}+\color{orange}{\frac{1}{7}}).(\color{green}{-b}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{1}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{17}x-\frac{1}{7}b+\frac{1}{7}.\frac{3}{17}& \text{Uitwerken } \\ & =-bx+\frac{3}{17}x-\frac{1}{7}b+\frac{3}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{12}{19})(\frac{-17}{8}-a)& =(\color{red}{q}+\color{orange}{\frac{12}{19}}).(\color{green}{-a}+\color{blue}{\frac{-17}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{8})} + \color{orange}{(\frac{12}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{-17}{8})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{17}{8}q-\frac{12}{19}a-\frac{12}{19}.\frac{17}{8}& \text{Uitwerken } \\ & =-aq-\frac{17}{8}q-\frac{12}{19}a-\frac{204}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{17}{8}q-\frac{12}{19}a-\frac{51}{38} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-16}{6}-q)(\frac{20}{17}+x)& =(\color{red}{-q}+\color{orange}{\frac{-8}{3}}).(\color{green}{x}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{20}{17}q-\frac{8}{3}x-\frac{8}{3}.\frac{20}{17}& \text{Uitwerken } \\ & =-qx-\frac{20}{17}q-\frac{8}{3}x-\frac{160}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{14}{8}+x)(q-\frac{-6}{6})& =(\color{red}{x}+\color{orange}{\frac{7}{4}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1x+\frac{7}{4}q+\frac{7}{4}.1& \text{Uitwerken } \\ & =qx+1x+\frac{7}{4}q+\frac{7}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-5}{9}+b)(\frac{2}{16}+a)& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{a}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{8}b-\frac{5}{9}a-\frac{5}{9}.\frac{1}{8}& \text{Uitwerken } \\ & =ab+\frac{1}{8}b-\frac{5}{9}a-\frac{5}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-5}{20}+b)(\frac{15}{19}-p)& =(\color{red}{b}+\color{orange}{\frac{-1}{4}}).(\color{green}{-p}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{15}{19}b+\frac{1}{4}p-\frac{1}{4}.\frac{15}{19}& \text{Uitwerken } \\ & =-bp+\frac{15}{19}b+\frac{1}{4}p-\frac{15}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{12}-b)(\frac{-17}{15}+b)& =(\color{red}{-b}+\color{orange}{\frac{-13}{12}}).(\color{green}{b}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{17}{15}b-\frac{13}{12}b+\frac{13}{12}.\frac{17}{15}& \text{Uitwerken } \\ & =-b^2+(\frac{17}{15}+(\frac{-13}{12}))b+(\frac{-221}{180}) & \text{Neem samen} \\ &=-b^2+\frac{3}{60}b+(\frac{-221}{180}) & \text{Maak de som} \\ &=-b^2+\frac{1}{20}b+(\frac{-221}{180}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(p-\frac{1}{10})(q-\frac{12}{3})& =(\color{red}{p}+\color{orange}{\frac{-1}{10}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{-1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = pq-4p-\frac{1}{10}q+\frac{1}{10}.4& \text{Uitwerken } \\ & =pq-4p-\frac{1}{10}q+\frac{4}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-4p-\frac{1}{10}q+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
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