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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{13}{3})(\frac{-7}{19}+b)& =(\color{red}{q}+\color{orange}{\frac{13}{3}}).(\color{green}{b}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{13}{3})} . \color{green}{(b)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{19}q+\frac{13}{3}b-\frac{13}{3}.\frac{7}{19}& \text{Uitwerken } \\ & =bq-\frac{7}{19}q+\frac{13}{3}b-\frac{91}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{1}{20})(a+\frac{-12}{10})& =(\color{red}{b}+\color{orange}{\frac{1}{20}}).(\color{green}{a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{1}{20})} . \color{green}{(a)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{6}{5}b+\frac{1}{20}a-\frac{1}{20}.\frac{6}{5}& \text{Uitwerken } \\ & =ab-\frac{6}{5}b+\frac{1}{20}a-\frac{6}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{6}{5}b+\frac{1}{20}a-\frac{3}{50} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-12}{8})(a+\frac{-1}{15})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{15}q-\frac{3}{2}a+\frac{3}{2}.\frac{1}{15}& \text{Uitwerken } \\ & =aq-\frac{1}{15}q-\frac{3}{2}a+\frac{3}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{15}q-\frac{3}{2}a+\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-8}{10}+q)(q-\frac{-10}{12})& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{6}q-\frac{4}{5}q-\frac{4}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =q^2+(\frac{5}{6}+(\frac{-4}{5}))q-(\frac{-20}{30}) & \text{Neem samen} \\ &=q^2+\frac{1}{30}q-(\frac{-20}{30}) & \text{Maak de som} \\ &=q^2+\frac{1}{30}q+\frac{2}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{2}+p)(q+\frac{-16}{11})& =(\color{red}{p}+\color{orange}{\frac{-9}{2}}).(\color{green}{q}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{16}{11}p-\frac{9}{2}q+\frac{9}{2}.\frac{16}{11}& \text{Uitwerken } \\ & =pq-\frac{16}{11}p-\frac{9}{2}q+\frac{144}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{16}{11}p-\frac{9}{2}q+\frac{72}{11} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-5}{17}-b)(b-\frac{-1}{19})& =(\color{red}{-b}+\color{orange}{\frac{-5}{17}}).(\color{green}{b}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{19}b-\frac{5}{17}b-\frac{5}{17}.\frac{1}{19}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{19})+(\frac{-5}{17}))b-\frac{5}{323} & \text{Neem samen} \\ &=-b^2-\frac{112}{323}b-\frac{5}{323} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-5}{9}-a)(p+\frac{7}{15})& =(\color{red}{-a}+\color{orange}{\frac{-5}{9}}).(\color{green}{p}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{15}a-\frac{5}{9}p-\frac{5}{9}.\frac{7}{15}& \text{Uitwerken } \\ & =-ap-\frac{7}{15}a-\frac{5}{9}p-\frac{35}{135} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{7}{15}a-\frac{5}{9}p-\frac{7}{27} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-4}{17})(p-\frac{12}{13})& =(\color{red}{a}+\color{orange}{\frac{4}{17}}).(\color{green}{p}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{4}{17})} . \color{green}{(p)} + \color{orange}{(\frac{4}{17})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{12}{13}a+\frac{4}{17}p-\frac{4}{17}.\frac{12}{13}& \text{Uitwerken } \\ & =ap-\frac{12}{13}a+\frac{4}{17}p-\frac{48}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-13)(\frac{11}{12}-x)& =(\color{red}{x}+\color{orange}{(-13)}).(\color{green}{-x}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(-13)} . \color{green}{(-x)} + \color{orange}{(-13)} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{11}{12}x+13x-13.\frac{11}{12}& \text{Uitwerken } \\ & =-x^2+(\frac{11}{12}+13)x-\frac{143}{12} & \text{Neem samen} \\ &=-x^2+\frac{167}{12}x-\frac{143}{12} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-15}{4}+p)(\frac{19}{12}+b)& =(\color{red}{p}+\color{orange}{\frac{-15}{4}}).(\color{green}{b}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{12}p-\frac{15}{4}b-\frac{15}{4}.\frac{19}{12}& \text{Uitwerken } \\ & =bp+\frac{19}{12}p-\frac{15}{4}b-\frac{285}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{19}{12}p-\frac{15}{4}b-\frac{95}{16} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p+\frac{6}{5})(b-\frac{10}{20})& =(\color{red}{p}+\color{orange}{\frac{6}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{2}p+\frac{6}{5}b-\frac{6}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =bp-\frac{1}{2}p+\frac{6}{5}b-\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{1}{2}p+\frac{6}{5}b-\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-13}{2}-p)(x+\frac{17}{16})& =(\color{red}{-p}+\color{orange}{\frac{-13}{2}}).(\color{green}{x}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{17}{16}p-\frac{13}{2}x-\frac{13}{2}.\frac{17}{16}& \text{Uitwerken } \\ & =-px-\frac{17}{16}p-\frac{13}{2}x-\frac{221}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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