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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{14}{2})(a-\frac{-16}{20})& =(\color{red}{b}+\color{orange}{7}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(7)} . \color{green}{(a)} + \color{orange}{(7)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{5}b+7a+7.\frac{4}{5}& \text{Uitwerken } \\ & =ab+\frac{4}{5}b+7a+\frac{28}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{1}{10}+a)(q+\frac{-13}{15})& =(\color{red}{a}+\color{orange}{\frac{1}{10}}).(\color{green}{q}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{15}a+\frac{1}{10}q-\frac{1}{10}.\frac{13}{15}& \text{Uitwerken } \\ & =aq-\frac{13}{15}a+\frac{1}{10}q-\frac{13}{150} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{8}{14}+q)(b+\frac{2}{20})& =(\color{red}{q}+\color{orange}{\frac{4}{7}}).(\color{green}{b}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{4}{7})} . \color{green}{(b)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{10}q+\frac{4}{7}b+\frac{4}{7}.\frac{1}{10}& \text{Uitwerken } \\ & =bq+\frac{1}{10}q+\frac{4}{7}b+\frac{4}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{10}q+\frac{4}{7}b+\frac{2}{35} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b-\frac{3}{20})((-16)-a)& =(\color{red}{b}+\color{orange}{\frac{-3}{20}}).(\color{green}{-a}+\color{blue}{(-16)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-16)} + \color{orange}{(\frac{-3}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = -ab-16b+\frac{3}{20}a+\frac{3}{20}.16& \text{Uitwerken } \\ & =-ab-16b+\frac{3}{20}a+\frac{48}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-16b+\frac{3}{20}a+\frac{12}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-3}{6})(a+\frac{19}{16})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{16}p+\frac{1}{2}a+\frac{1}{2}.\frac{19}{16}& \text{Uitwerken } \\ & =ap+\frac{19}{16}p+\frac{1}{2}a+\frac{19}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{15}{12})(\frac{16}{9}+q)& =(\color{red}{b}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{16}{9}b-\frac{5}{4}q-\frac{5}{4}.\frac{16}{9}& \text{Uitwerken } \\ & =bq+\frac{16}{9}b-\frac{5}{4}q-\frac{80}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{16}{9}b-\frac{5}{4}q-\frac{20}{9} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-1}{19}+q)(\frac{-11}{8}+x)& =(\color{red}{q}+\color{orange}{\frac{-1}{19}}).(\color{green}{x}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-1}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{8}q-\frac{1}{19}x+\frac{1}{19}.\frac{11}{8}& \text{Uitwerken } \\ & =qx-\frac{11}{8}q-\frac{1}{19}x+\frac{11}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-6}{6})(p-\frac{-14}{11})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{14}{11}a-1p-1.\frac{14}{11}& \text{Uitwerken } \\ & =ap+\frac{14}{11}a-1p-\frac{14}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-7}{15})(a-\frac{-15}{8})& =(\color{red}{p}+\color{orange}{\frac{-7}{15}}).(\color{green}{a}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{15}{8}p-\frac{7}{15}a-\frac{7}{15}.\frac{15}{8}& \text{Uitwerken } \\ & =ap+\frac{15}{8}p-\frac{7}{15}a-\frac{105}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{15}{8}p-\frac{7}{15}a-\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-6}{10})(\frac{20}{12}+a)& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{3}b+\frac{3}{5}a+\frac{3}{5}.\frac{5}{3}& \text{Uitwerken } \\ & =ab+\frac{5}{3}b+\frac{3}{5}a+\frac{15}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{5}{3}b+\frac{3}{5}a+1 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{16}+x)(x+\frac{-7}{19})& =(\color{red}{x}+\color{orange}{\frac{-19}{16}}).(\color{green}{x}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{7}{19}x-\frac{19}{16}x+\frac{19}{16}.\frac{7}{19}& \text{Uitwerken } \\ & =x^2+((\frac{-7}{19})+(\frac{-19}{16}))x+\frac{133}{304} & \text{Neem samen} \\ &=x^2-\frac{473}{304}x+\frac{133}{304} & \text{Maak de som} \\ &=x^2-\frac{473}{304}x+\frac{7}{16} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{17}+q)(p-\frac{-1}{18})& =(\color{red}{q}+\color{orange}{\frac{8}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{8}{17})} . \color{green}{(p)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{18}q+\frac{8}{17}p+\frac{8}{17}.\frac{1}{18}& \text{Uitwerken } \\ & =pq+\frac{1}{18}q+\frac{8}{17}p+\frac{8}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{18}q+\frac{8}{17}p+\frac{4}{153} & \text{Vereenvoudig} \\\end{align}\)
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