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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{10}-b)(\frac{8}{13}+p)& =(\color{red}{-b}+\color{orange}{\frac{8}{5}}).(\color{green}{p}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{8}{5})} . \color{green}{(p)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{8}{13}b+\frac{8}{5}p+\frac{8}{5}.\frac{8}{13}& \text{Uitwerken } \\ & =-bp-\frac{8}{13}b+\frac{8}{5}p+\frac{64}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{17}+p)(\frac{-14}{3}+x)& =(\color{red}{p}+\color{orange}{\frac{15}{17}}).(\color{green}{x}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(\frac{15}{17})} . \color{green}{(x)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{14}{3}p+\frac{15}{17}x-\frac{15}{17}.\frac{14}{3}& \text{Uitwerken } \\ & =px-\frac{14}{3}p+\frac{15}{17}x-\frac{210}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{14}{3}p+\frac{15}{17}x-\frac{70}{17} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{13}{18})(b-\frac{3}{8})& =(\color{red}{b}+\color{orange}{\frac{13}{18}}).(\color{green}{b}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{13}{18})} . \color{green}{(b)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{8}b+\frac{13}{18}b-\frac{13}{18}.\frac{3}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{8})+\frac{13}{18})b-(\frac{-39}{144}) & \text{Neem samen} \\ &=b^2+\frac{25}{72}b-(\frac{-39}{144}) & \text{Maak de som} \\ &=b^2+\frac{25}{72}b+\frac{13}{48} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(p-\frac{9}{5})(p+\frac{-10}{15})& =(\color{red}{p}+\color{orange}{\frac{-9}{5}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{2}{3}p-\frac{9}{5}p+\frac{9}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-2}{3})+(\frac{-9}{5}))p+\frac{18}{15} & \text{Neem samen} \\ &=p^2-\frac{37}{15}p+\frac{18}{15} & \text{Maak de som} \\ &=p^2-\frac{37}{15}p+\frac{6}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{2}+a)(a+\frac{4}{10})& =(\color{red}{a}+\color{orange}{8}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(8)} . \color{green}{(a)} + \color{orange}{(8)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{2}{5}a+8a+8.\frac{2}{5}& \text{Uitwerken } \\ & =a^2+(\frac{2}{5}+8)a+\frac{16}{5} & \text{Neem samen} \\ &=a^2+\frac{42}{5}a+\frac{16}{5} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{17}{12}-q)(\frac{6}{17}-x)& =(\color{red}{-q}+\color{orange}{\frac{17}{12}}).(\color{green}{-x}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{17}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{6}{17}q-\frac{17}{12}x+\frac{17}{12}.\frac{6}{17}& \text{Uitwerken } \\ & =qx-\frac{6}{17}q-\frac{17}{12}x+\frac{102}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{6}{17}q-\frac{17}{12}x+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{11}{15})(\frac{-14}{19}-b)& =(\color{red}{b}+\color{orange}{\frac{11}{15}}).(\color{green}{-b}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{11}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{14}{19}b-\frac{11}{15}b-\frac{11}{15}.\frac{14}{19}& \text{Uitwerken } \\ & =-b^2+((\frac{-14}{19})+(\frac{-11}{15}))b-\frac{154}{285} & \text{Neem samen} \\ &=-b^2-\frac{419}{285}b-\frac{154}{285} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{15}-a)(\frac{-1}{13}+b)& =(\color{red}{-a}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{13}a+\frac{4}{5}b-\frac{4}{5}.\frac{1}{13}& \text{Uitwerken } \\ & =-ab+\frac{1}{13}a+\frac{4}{5}b-\frac{4}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{13}{12})(p-\frac{20}{8})& =(\color{red}{q}+\color{orange}{\frac{13}{12}}).(\color{green}{p}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{13}{12})} . \color{green}{(p)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{2}q+\frac{13}{12}p-\frac{13}{12}.\frac{5}{2}& \text{Uitwerken } \\ & =pq-\frac{5}{2}q+\frac{13}{12}p-\frac{65}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-6}{2})(q+\frac{-17}{6})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{q}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(-3)} . \color{green}{(q)} + \color{orange}{(-3)} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{17}{6}q-3q+3.\frac{17}{6}& \text{Uitwerken } \\ & =q^2+((\frac{-17}{6})+(-3))q+\frac{51}{6} & \text{Neem samen} \\ &=q^2-\frac{35}{6}q+\frac{51}{6} & \text{Maak de som} \\ &=q^2-\frac{35}{6}q+\frac{17}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{17}-x)(p+\frac{-6}{7})& =(\color{red}{-x}+\color{orange}{\frac{10}{17}}).(\color{green}{p}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{10}{17})} . \color{green}{(p)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{6}{7}x+\frac{10}{17}p-\frac{10}{17}.\frac{6}{7}& \text{Uitwerken } \\ & =-px+\frac{6}{7}x+\frac{10}{17}p-\frac{60}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{6}+p)(\frac{3}{3}-p)& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pp+1p+\frac{3}{2}p-\frac{3}{2}.1& \text{Uitwerken } \\ & =-p^2+(1+\frac{3}{2})p-\frac{3}{2} & \text{Neem samen} \\ &=-p^2+\frac{5}{2}p-\frac{3}{2} & \text{Maak de som} \\\end{align}\)
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