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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{20}{15})(a+\frac{-2}{16})& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{a}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{8}b-\frac{4}{3}a+\frac{4}{3}.\frac{1}{8}& \text{Uitwerken } \\ & =ab-\frac{1}{8}b-\frac{4}{3}a+\frac{4}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{8}b-\frac{4}{3}a+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{13}+b)(q+\frac{-11}{10})& =(\color{red}{b}+\color{orange}{\frac{20}{13}}).(\color{green}{q}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{10})} + \color{orange}{(\frac{20}{13})} . \color{green}{(q)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{10}b+\frac{20}{13}q-\frac{20}{13}.\frac{11}{10}& \text{Uitwerken } \\ & =bq-\frac{11}{10}b+\frac{20}{13}q-\frac{220}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{11}{10}b+\frac{20}{13}q-\frac{22}{13} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{18}{11}+x)(b+\frac{13}{3})& =(\color{red}{x}+\color{orange}{\frac{18}{11}}).(\color{green}{b}+\color{blue}{\frac{13}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{13}{3})} + \color{orange}{(\frac{18}{11})} . \color{green}{(b)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{13}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{3}x+\frac{18}{11}b+\frac{18}{11}.\frac{13}{3}& \text{Uitwerken } \\ & =bx+\frac{13}{3}x+\frac{18}{11}b+\frac{234}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{13}{3}x+\frac{18}{11}b+\frac{78}{11} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{13}+a)(a+\frac{-18}{16})& =(\color{red}{a}+\color{orange}{\frac{-2}{13}}).(\color{green}{a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{9}{8}a-\frac{2}{13}a+\frac{2}{13}.\frac{9}{8}& \text{Uitwerken } \\ & =a^2+((\frac{-9}{8})+(\frac{-2}{13}))a+\frac{18}{104} & \text{Neem samen} \\ &=a^2-\frac{133}{104}a+\frac{18}{104} & \text{Maak de som} \\ &=a^2-\frac{133}{104}a+\frac{9}{52} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{20}{18}+x)(\frac{3}{2}-q)& =(\color{red}{x}+\color{orange}{\frac{10}{9}}).(\color{green}{-q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{10}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{2}x-\frac{10}{9}q+\frac{10}{9}.\frac{3}{2}& \text{Uitwerken } \\ & =-qx+\frac{3}{2}x-\frac{10}{9}q+\frac{30}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{3}{2}x-\frac{10}{9}q+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{9}{5})(q+\frac{8}{9})& =(\color{red}{b}+\color{orange}{\frac{-9}{5}}).(\color{green}{q}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{9}b-\frac{9}{5}q-\frac{9}{5}.\frac{8}{9}& \text{Uitwerken } \\ & =bq+\frac{8}{9}b-\frac{9}{5}q-\frac{72}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{8}{9}b-\frac{9}{5}q-\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{12}{12}+p)(a+\frac{9}{15})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{5}p+1a+1.\frac{3}{5}& \text{Uitwerken } \\ & =ap+\frac{3}{5}p+1a+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{12}{17})(\frac{-7}{6}-x)& =(\color{red}{b}+\color{orange}{\frac{-12}{17}}).(\color{green}{-x}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{7}{6}b+\frac{12}{17}x+\frac{12}{17}.\frac{7}{6}& \text{Uitwerken } \\ & =-bx-\frac{7}{6}b+\frac{12}{17}x+\frac{84}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{7}{6}b+\frac{12}{17}x+\frac{14}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{1}{20})(b-\frac{18}{5})& =(\color{red}{p}+\color{orange}{\frac{-1}{20}}).(\color{green}{b}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{-1}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{18}{5}p-\frac{1}{20}b+\frac{1}{20}.\frac{18}{5}& \text{Uitwerken } \\ & =bp-\frac{18}{5}p-\frac{1}{20}b+\frac{18}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{18}{5}p-\frac{1}{20}b+\frac{9}{50} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-3}{8}+b)(q+\frac{16}{8})& =(\color{red}{b}+\color{orange}{\frac{-3}{8}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{-3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bq+2b-\frac{3}{8}q-\frac{3}{8}.2& \text{Uitwerken } \\ & =bq+2b-\frac{3}{8}q-\frac{6}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+2b-\frac{3}{8}q-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-1}{16}-a)(\frac{-14}{16}-a)& =(\color{red}{-a}+\color{orange}{\frac{-1}{16}}).(\color{green}{-a}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{8}a+\frac{1}{16}a+\frac{1}{16}.\frac{7}{8}& \text{Uitwerken } \\ & =a^2+(\frac{7}{8}+\frac{1}{16})a+\frac{7}{128} & \text{Neem samen} \\ &=a^2+\frac{15}{16}a+\frac{7}{128} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-7}{17})(q+\frac{-20}{3})& =(\color{red}{q}+\color{orange}{\frac{-7}{17}}).(\color{green}{q}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{20}{3}q-\frac{7}{17}q+\frac{7}{17}.\frac{20}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-20}{3})+(\frac{-7}{17}))q+\frac{140}{51} & \text{Neem samen} \\ &=q^2-\frac{361}{51}q+\frac{140}{51} & \text{Maak de som} \\\end{align}\)
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