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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{13}{18})(\frac{-16}{5}-a)& =(\color{red}{b}+\color{orange}{\frac{13}{18}}).(\color{green}{-a}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{13}{18})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{16}{5}b-\frac{13}{18}a-\frac{13}{18}.\frac{16}{5}& \text{Uitwerken } \\ & =-ab-\frac{16}{5}b-\frac{13}{18}a-\frac{208}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{16}{5}b-\frac{13}{18}a-\frac{104}{45} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{3}{10}+a)(\frac{-2}{10}+a)& =(\color{red}{a}+\color{orange}{\frac{3}{10}}).(\color{green}{a}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{5}a+\frac{3}{10}a-\frac{3}{10}.\frac{1}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{5})+\frac{3}{10})a-(\frac{-3}{50}) & \text{Neem samen} \\ &=a^2+\frac{1}{10}a-(\frac{-3}{50}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-6}{11}-x)(q-\frac{2}{18})& =(\color{red}{-x}+\color{orange}{\frac{-6}{11}}).(\color{green}{q}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{9}x-\frac{6}{11}q+\frac{6}{11}.\frac{1}{9}& \text{Uitwerken } \\ & =-qx+\frac{1}{9}x-\frac{6}{11}q+\frac{6}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{1}{9}x-\frac{6}{11}q+\frac{2}{33} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-9}{19})(\frac{-1}{18}-p)& =(\color{red}{x}+\color{orange}{\frac{9}{19}}).(\color{green}{-p}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{9}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{18}x-\frac{9}{19}p-\frac{9}{19}.\frac{1}{18}& \text{Uitwerken } \\ & =-px-\frac{1}{18}x-\frac{9}{19}p-\frac{9}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{1}{18}x-\frac{9}{19}p-\frac{1}{38} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-\frac{14}{7})(p-\frac{-9}{2})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{2}b-2p-2.\frac{9}{2}& \text{Uitwerken } \\ & =bp+\frac{9}{2}b-2p-\frac{18}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{2}b-2p-9 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{12}-b)(b-\frac{8}{14})& =(\color{red}{-b}+\color{orange}{\frac{-11}{12}}).(\color{green}{b}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{4}{7}b-\frac{11}{12}b+\frac{11}{12}.\frac{4}{7}& \text{Uitwerken } \\ & =-b^2+(\frac{4}{7}+(\frac{-11}{12}))b+(\frac{-44}{84}) & \text{Neem samen} \\ &=-b^2-\frac{29}{84}b+(\frac{-44}{84}) & \text{Maak de som} \\ &=-b^2-\frac{29}{84}b+(\frac{-11}{21}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{-1}{15}+a)(\frac{7}{9}+b)& =(\color{red}{a}+\color{orange}{\frac{-1}{15}}).(\color{green}{b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{9}a-\frac{1}{15}b-\frac{1}{15}.\frac{7}{9}& \text{Uitwerken } \\ & =ab+\frac{7}{9}a-\frac{1}{15}b-\frac{7}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{16}{17})(x-\frac{10}{9})& =(\color{red}{p}+\color{orange}{\frac{16}{17}}).(\color{green}{x}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{16}{17})} . \color{green}{(x)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{9}p+\frac{16}{17}x-\frac{16}{17}.\frac{10}{9}& \text{Uitwerken } \\ & =px-\frac{10}{9}p+\frac{16}{17}x-\frac{160}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{2}{12}-p)(\frac{7}{13}-a)& =(\color{red}{-p}+\color{orange}{\frac{1}{6}}).(\color{green}{-a}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{1}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{13}p-\frac{1}{6}a+\frac{1}{6}.\frac{7}{13}& \text{Uitwerken } \\ & =ap-\frac{7}{13}p-\frac{1}{6}a+\frac{7}{78} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{5}{10}-a)(x+\frac{4}{6})& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{2}{3}a+\frac{1}{2}x+\frac{1}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =-ax-\frac{2}{3}a+\frac{1}{2}x+\frac{2}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{2}{3}a+\frac{1}{2}x+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{2}{20}+q)(x-\frac{15}{8})& =(\color{red}{q}+\color{orange}{\frac{1}{10}}).(\color{green}{x}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{15}{8}q+\frac{1}{10}x-\frac{1}{10}.\frac{15}{8}& \text{Uitwerken } \\ & =qx-\frac{15}{8}q+\frac{1}{10}x-\frac{15}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{15}{8}q+\frac{1}{10}x-\frac{3}{16} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-8}{15})(x-\frac{-13}{20})& =(\color{red}{q}+\color{orange}{\frac{-8}{15}}).(\color{green}{x}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{20}q-\frac{8}{15}x-\frac{8}{15}.\frac{13}{20}& \text{Uitwerken } \\ & =qx+\frac{13}{20}q-\frac{8}{15}x-\frac{104}{300} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{13}{20}q-\frac{8}{15}x-\frac{26}{75} & \text{Vereenvoudig} \\\end{align}\)
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