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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-20}{20}-x)(\frac{-12}{11}+x)& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{12}{11}x-1x+1.\frac{12}{11}& \text{Uitwerken } \\ & =-x^2+(\frac{12}{11}+(-1))x+(\frac{-12}{11}) & \text{Neem samen} \\ &=-x^2+\frac{1}{11}x+(\frac{-12}{11}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(p+\frac{15}{4})(\frac{-20}{7}+b)& =(\color{red}{p}+\color{orange}{\frac{15}{4}}).(\color{green}{b}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{15}{4})} . \color{green}{(b)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{20}{7}p+\frac{15}{4}b-\frac{15}{4}.\frac{20}{7}& \text{Uitwerken } \\ & =bp-\frac{20}{7}p+\frac{15}{4}b-\frac{300}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{20}{7}p+\frac{15}{4}b-\frac{75}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{6}{20})(\frac{-6}{15}+a)& =(\color{red}{b}+\color{orange}{\frac{-3}{10}}).(\color{green}{a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{5}b-\frac{3}{10}a+\frac{3}{10}.\frac{2}{5}& \text{Uitwerken } \\ & =ab-\frac{2}{5}b-\frac{3}{10}a+\frac{6}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{2}{5}b-\frac{3}{10}a+\frac{3}{25} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{18}{5}-b)(a-\frac{9}{10})& =(\color{red}{-b}+\color{orange}{\frac{18}{5}}).(\color{green}{a}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{18}{5})} . \color{green}{(a)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{9}{10}b+\frac{18}{5}a-\frac{18}{5}.\frac{9}{10}& \text{Uitwerken } \\ & =-ab+\frac{9}{10}b+\frac{18}{5}a-\frac{162}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{9}{10}b+\frac{18}{5}a-\frac{81}{25} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{11}{2}-a)(\frac{16}{15}-a)& =(\color{red}{-a}+\color{orange}{\frac{11}{2}}).(\color{green}{-a}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{11}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{16}{15}a-\frac{11}{2}a+\frac{11}{2}.\frac{16}{15}& \text{Uitwerken } \\ & =a^2+((\frac{-16}{15})+(\frac{-11}{2}))a+\frac{176}{30} & \text{Neem samen} \\ &=a^2-\frac{197}{30}a+\frac{176}{30} & \text{Maak de som} \\ &=a^2-\frac{197}{30}a+\frac{88}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-3}{18}+p)(\frac{-19}{5}+b)& =(\color{red}{p}+\color{orange}{\frac{-1}{6}}).(\color{green}{b}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{5}p-\frac{1}{6}b+\frac{1}{6}.\frac{19}{5}& \text{Uitwerken } \\ & =bp-\frac{19}{5}p-\frac{1}{6}b+\frac{19}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-14}{20})(17+a)& =(\color{red}{p}+\color{orange}{\frac{7}{10}}).(\color{green}{a}+\color{blue}{17})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(17)} + \color{orange}{(\frac{7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = ap+17p+\frac{7}{10}a+\frac{7}{10}.17& \text{Uitwerken } \\ & =ap+17p+\frac{7}{10}a+\frac{119}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-6}{20}-b)(q-\frac{14}{12})& =(\color{red}{-b}+\color{orange}{\frac{-3}{10}}).(\color{green}{q}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{6}b-\frac{3}{10}q+\frac{3}{10}.\frac{7}{6}& \text{Uitwerken } \\ & =-bq+\frac{7}{6}b-\frac{3}{10}q+\frac{21}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{7}{6}b-\frac{3}{10}q+\frac{7}{20} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{20}{18})(a+\frac{-3}{20})& =(\color{red}{x}+\color{orange}{\frac{10}{9}}).(\color{green}{a}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{20}x+\frac{10}{9}a-\frac{10}{9}.\frac{3}{20}& \text{Uitwerken } \\ & =ax-\frac{3}{20}x+\frac{10}{9}a-\frac{30}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{3}{20}x+\frac{10}{9}a-\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b+\frac{4}{20})(\frac{19}{12}+x)& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{x}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{12}b+\frac{1}{5}x+\frac{1}{5}.\frac{19}{12}& \text{Uitwerken } \\ & =bx+\frac{19}{12}b+\frac{1}{5}x+\frac{19}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{18}{18})(x-\frac{-7}{19})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{7}{19}x+1x+1.\frac{7}{19}& \text{Uitwerken } \\ & =x^2+(\frac{7}{19}+1)x+\frac{7}{19} & \text{Neem samen} \\ &=x^2+\frac{26}{19}x+\frac{7}{19} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q-\frac{10}{5})(q+\frac{10}{2})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = qq+5q-2q-2.5& \text{Uitwerken } \\ & =q^2+(5+(-2))q-(-10) & \text{Neem samen} \\ &=q^2+3q-(-10) & \text{Maak de som} \\\end{align}\)
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