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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{3}{14})(b+\frac{13}{6})& =(\color{red}{x}+\color{orange}{\frac{-3}{14}}).(\color{green}{b}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{-3}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{14})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{6}x-\frac{3}{14}b-\frac{3}{14}.\frac{13}{6}& \text{Uitwerken } \\ & =bx+\frac{13}{6}x-\frac{3}{14}b-\frac{39}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{13}{6}x-\frac{3}{14}b-\frac{13}{28} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-20}{16})(q-\frac{17}{12})& =(\color{red}{p}+\color{orange}{\frac{5}{4}}).(\color{green}{q}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{12}p+\frac{5}{4}q-\frac{5}{4}.\frac{17}{12}& \text{Uitwerken } \\ & =pq-\frac{17}{12}p+\frac{5}{4}q-\frac{85}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{19}-p)(\frac{4}{20}+b)& =(\color{red}{-p}+\color{orange}{\frac{-18}{19}}).(\color{green}{b}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{5}p-\frac{18}{19}b-\frac{18}{19}.\frac{1}{5}& \text{Uitwerken } \\ & =-bp-\frac{1}{5}p-\frac{18}{19}b-\frac{18}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-12}{10}+p)(b+\frac{7}{8})& =(\color{red}{p}+\color{orange}{\frac{-6}{5}}).(\color{green}{b}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{8}p-\frac{6}{5}b-\frac{6}{5}.\frac{7}{8}& \text{Uitwerken } \\ & =bp+\frac{7}{8}p-\frac{6}{5}b-\frac{42}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{7}{8}p-\frac{6}{5}b-\frac{21}{20} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{8}-x)(b+\frac{6}{20})& =(\color{red}{-x}+\color{orange}{\frac{-9}{8}}).(\color{green}{b}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{10}x-\frac{9}{8}b-\frac{9}{8}.\frac{3}{10}& \text{Uitwerken } \\ & =-bx-\frac{3}{10}x-\frac{9}{8}b-\frac{27}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(18-q)(q-\frac{-15}{8})& =(\color{red}{-q}+\color{orange}{18}).(\color{green}{q}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(18)} . \color{green}{(q)} + \color{orange}{(18)} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{15}{8}q+18q+18.\frac{15}{8}& \text{Uitwerken } \\ & =-q^2+((\frac{-15}{8})+18)q+(\frac{-270}{8}) & \text{Neem samen} \\ &=-q^2+\frac{129}{8}q+(\frac{-270}{8}) & \text{Maak de som} \\ &=-q^2+\frac{129}{8}q+(\frac{-135}{4}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(b-\frac{19}{5})(x+\frac{19}{5})& =(\color{red}{b}+\color{orange}{\frac{-19}{5}}).(\color{green}{x}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{5}b-\frac{19}{5}x-\frac{19}{5}.\frac{19}{5}& \text{Uitwerken } \\ & =bx+\frac{19}{5}b-\frac{19}{5}x-\frac{361}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{5}{16}-a)(p+\frac{-12}{9})& =(\color{red}{-a}+\color{orange}{\frac{5}{16}}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{5}{16})} . \color{green}{(p)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{4}{3}a+\frac{5}{16}p-\frac{5}{16}.\frac{4}{3}& \text{Uitwerken } \\ & =-ap+\frac{4}{3}a+\frac{5}{16}p-\frac{20}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{4}{3}a+\frac{5}{16}p-\frac{5}{12} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{8}{20}-p)(6-a)& =(\color{red}{-p}+\color{orange}{\frac{2}{5}}).(\color{green}{-a}+\color{blue}{6})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(6)} + \color{orange}{(\frac{2}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = ap-6p-\frac{2}{5}a+\frac{2}{5}.6& \text{Uitwerken } \\ & =ap-6p-\frac{2}{5}a+\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-15}{4})(2+x)& =(\color{red}{p}+\color{orange}{\frac{-15}{4}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-15}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = px+2p-\frac{15}{4}x-\frac{15}{4}.2& \text{Uitwerken } \\ & =px+2p-\frac{15}{4}x-\frac{30}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+2p-\frac{15}{4}x-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{12}{20}-q)(\frac{4}{4}-q)& =(\color{red}{-q}+\color{orange}{\frac{3}{5}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qq-1q-\frac{3}{5}q+\frac{3}{5}.1& \text{Uitwerken } \\ & =q^2+((-1)+(\frac{-3}{5}))q+\frac{3}{5} & \text{Neem samen} \\ &=q^2-\frac{8}{5}q+\frac{3}{5} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-16}{6})(\frac{-2}{14}-b)& =(\color{red}{a}+\color{orange}{\frac{8}{3}}).(\color{green}{-b}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{8}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{7}a-\frac{8}{3}b-\frac{8}{3}.\frac{1}{7}& \text{Uitwerken } \\ & =-ab-\frac{1}{7}a-\frac{8}{3}b-\frac{8}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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