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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{14}-p)(p-\frac{8}{20})& =(\color{red}{-p}+\color{orange}{\frac{8}{7}}).(\color{green}{p}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{2}{5}p+\frac{8}{7}p-\frac{8}{7}.\frac{2}{5}& \text{Uitwerken } \\ & =-p^2+(\frac{2}{5}+\frac{8}{7})p-\frac{16}{35} & \text{Neem samen} \\ &=-p^2+\frac{54}{35}p-\frac{16}{35} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(a+\frac{14}{14})(x-\frac{-15}{6})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{2}a+1x+1.\frac{5}{2}& \text{Uitwerken } \\ & =ax+\frac{5}{2}a+1x+\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{11}{18})(p+\frac{18}{9})& =(\color{red}{q}+\color{orange}{\frac{11}{18}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{11}{18})} . \color{green}{(p)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2q+\frac{11}{18}p+\frac{11}{18}.2& \text{Uitwerken } \\ & =pq+2q+\frac{11}{18}p+\frac{22}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+2q+\frac{11}{18}p+\frac{11}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-17}{4})(b+(-19))& =(\color{red}{a}+\color{orange}{\frac{17}{4}}).(\color{green}{b}+\color{blue}{(-19)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-19)} + \color{orange}{(\frac{17}{4})} . \color{green}{(b)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = ab-19a+\frac{17}{4}b-\frac{17}{4}.19& \text{Uitwerken } \\ & =ab-19a+\frac{17}{4}b-\frac{323}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{13}{12})(q-\frac{16}{17})& =(\color{red}{q}+\color{orange}{\frac{13}{12}}).(\color{green}{q}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{13}{12})} . \color{green}{(q)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{16}{17}q+\frac{13}{12}q-\frac{13}{12}.\frac{16}{17}& \text{Uitwerken } \\ & =q^2+((\frac{-16}{17})+\frac{13}{12})q-(\frac{-208}{204}) & \text{Neem samen} \\ &=q^2+\frac{29}{204}q-(\frac{-208}{204}) & \text{Maak de som} \\ &=q^2+\frac{29}{204}q+\frac{52}{51} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(b+\frac{19}{11})(\frac{-16}{2}+b)& =(\color{red}{b}+\color{orange}{\frac{19}{11}}).(\color{green}{b}+\color{blue}{(-8)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-8)} + \color{orange}{(\frac{19}{11})} . \color{green}{(b)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = bb-8b+\frac{19}{11}b-\frac{19}{11}.8& \text{Uitwerken } \\ & =b^2+((-8)+\frac{19}{11})b-(\frac{-152}{11}) & \text{Neem samen} \\ &=b^2-\frac{69}{11}b-(\frac{-152}{11}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-18}{18})(b-\frac{-9}{7})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{9}{7}b-1b-1.\frac{9}{7}& \text{Uitwerken } \\ & =b^2+(\frac{9}{7}+(-1))b-(\frac{-9}{7}) & \text{Neem samen} \\ &=b^2+\frac{2}{7}b-(\frac{-9}{7}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(q-\frac{3}{13})(p-\frac{-4}{10})& =(\color{red}{q}+\color{orange}{\frac{-3}{13}}).(\color{green}{p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{5}q-\frac{3}{13}p-\frac{3}{13}.\frac{2}{5}& \text{Uitwerken } \\ & =pq+\frac{2}{5}q-\frac{3}{13}p-\frac{6}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-8}{10})(x-\frac{-10}{12})& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{6}b-\frac{4}{5}x-\frac{4}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =bx+\frac{5}{6}b-\frac{4}{5}x-\frac{20}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{5}{6}b-\frac{4}{5}x-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-11}{16})(\frac{17}{18}-a)& =(\color{red}{b}+\color{orange}{\frac{11}{16}}).(\color{green}{-a}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{11}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{17}{18}b-\frac{11}{16}a+\frac{11}{16}.\frac{17}{18}& \text{Uitwerken } \\ & =-ab+\frac{17}{18}b-\frac{11}{16}a+\frac{187}{288} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{7}{14}-p)(\frac{-8}{6}+b)& =(\color{red}{-p}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{4}{3}p+\frac{1}{2}b-\frac{1}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =-bp+\frac{4}{3}p+\frac{1}{2}b-\frac{4}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{4}{3}p+\frac{1}{2}b-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a+12)(a-\frac{7}{8})& =(\color{red}{a}+\color{orange}{12}).(\color{green}{a}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(12)} . \color{green}{(a)} + \color{orange}{(12)} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{7}{8}a+12a-12.\frac{7}{8}& \text{Uitwerken } \\ & =a^2+((\frac{-7}{8})+12)a-(\frac{-84}{8}) & \text{Neem samen} \\ &=a^2+\frac{89}{8}a-(\frac{-84}{8}) & \text{Maak de som} \\ &=a^2+\frac{89}{8}a+\frac{21}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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