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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{20}{11})(\frac{12}{11}+p)& =(\color{red}{b}+\color{orange}{\frac{-20}{11}}).(\color{green}{p}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{12}{11}b-\frac{20}{11}p-\frac{20}{11}.\frac{12}{11}& \text{Uitwerken } \\ & =bp+\frac{12}{11}b-\frac{20}{11}p-\frac{240}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-3}{17})(\frac{-15}{9}+x)& =(\color{red}{b}+\color{orange}{\frac{3}{17}}).(\color{green}{x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{3}{17})} . \color{green}{(x)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{3}b+\frac{3}{17}x-\frac{3}{17}.\frac{5}{3}& \text{Uitwerken } \\ & =bx-\frac{5}{3}b+\frac{3}{17}x-\frac{15}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{5}{3}b+\frac{3}{17}x-\frac{5}{17} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-20}{3}-b)(\frac{-8}{8}-q)& =(\color{red}{-b}+\color{orange}{\frac{-20}{3}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-20}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b+\frac{20}{3}q+\frac{20}{3}.1& \text{Uitwerken } \\ & =bq+1b+\frac{20}{3}q+\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{8}{14})(b-\frac{-17}{17})& =(\color{red}{x}+\color{orange}{\frac{4}{7}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{4}{7})} . \color{green}{(b)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x+\frac{4}{7}b+\frac{4}{7}.1& \text{Uitwerken } \\ & =bx+1x+\frac{4}{7}b+\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{19}+q)(\frac{12}{14}+b)& =(\color{red}{q}+\color{orange}{\frac{-15}{19}}).(\color{green}{b}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{6}{7}q-\frac{15}{19}b-\frac{15}{19}.\frac{6}{7}& \text{Uitwerken } \\ & =bq+\frac{6}{7}q-\frac{15}{19}b-\frac{90}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-5}{18}-a)(b+\frac{2}{19})& =(\color{red}{-a}+\color{orange}{\frac{-5}{18}}).(\color{green}{b}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{19}a-\frac{5}{18}b-\frac{5}{18}.\frac{2}{19}& \text{Uitwerken } \\ & =-ab-\frac{2}{19}a-\frac{5}{18}b-\frac{10}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{2}{19}a-\frac{5}{18}b-\frac{5}{171} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{2}{14}-a)(\frac{20}{8}-p)& =(\color{red}{-a}+\color{orange}{\frac{1}{7}}).(\color{green}{-p}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{1}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{2}a-\frac{1}{7}p+\frac{1}{7}.\frac{5}{2}& \text{Uitwerken } \\ & =ap-\frac{5}{2}a-\frac{1}{7}p+\frac{5}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-5}{15})(b-\frac{4}{17})& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{17}a+\frac{1}{3}b-\frac{1}{3}.\frac{4}{17}& \text{Uitwerken } \\ & =ab-\frac{4}{17}a+\frac{1}{3}b-\frac{4}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-9}{4})(\frac{6}{4}+x)& =(\color{red}{x}+\color{orange}{\frac{9}{4}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{9}{4})} . \color{green}{(x)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{3}{2}x+\frac{9}{4}x+\frac{9}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =x^2+(\frac{3}{2}+\frac{9}{4})x+\frac{27}{8} & \text{Neem samen} \\ &=x^2+\frac{15}{4}x+\frac{27}{8} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-16}{13}+a)(\frac{19}{3}+x)& =(\color{red}{a}+\color{orange}{\frac{-16}{13}}).(\color{green}{x}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{3}a-\frac{16}{13}x-\frac{16}{13}.\frac{19}{3}& \text{Uitwerken } \\ & =ax+\frac{19}{3}a-\frac{16}{13}x-\frac{304}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{4}{6})(b-\frac{8}{9})& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{9}p-\frac{2}{3}b+\frac{2}{3}.\frac{8}{9}& \text{Uitwerken } \\ & =bp-\frac{8}{9}p-\frac{2}{3}b+\frac{16}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-20}{6}-a)(\frac{1}{2}-a)& =(\color{red}{-a}+\color{orange}{\frac{-10}{3}}).(\color{green}{-a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{2}a+\frac{10}{3}a-\frac{10}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{2})+\frac{10}{3})a-(\frac{-10}{6}) & \text{Neem samen} \\ &=a^2+\frac{17}{6}a-(\frac{-10}{6}) & \text{Maak de som} \\ &=a^2+\frac{17}{6}a+\frac{5}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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