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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-(-11))(b+\frac{3}{18})& =(\color{red}{x}+\color{orange}{11}).(\color{green}{b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(11)} . \color{green}{(b)} + \color{orange}{(11)} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{6}x+11b+11.\frac{1}{6}& \text{Uitwerken } \\ & =bx+\frac{1}{6}x+11b+\frac{11}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-20}{5}+a)(\frac{3}{10}+a)& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{10}a-4a-4.\frac{3}{10}& \text{Uitwerken } \\ & =a^2+(\frac{3}{10}+(-4))a-(\frac{-12}{10}) & \text{Neem samen} \\ &=a^2-\frac{37}{10}a-(\frac{-12}{10}) & \text{Maak de som} \\ &=a^2-\frac{37}{10}a+\frac{6}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(b-(-18))(x-\frac{-15}{17})& =(\color{red}{b}+\color{orange}{18}).(\color{green}{x}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(18)} . \color{green}{(x)} + \color{orange}{(18)} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{17}b+18x+18.\frac{15}{17}& \text{Uitwerken } \\ & =bx+\frac{15}{17}b+18x+\frac{270}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{11}{14})(\frac{10}{2}+b)& =(\color{red}{p}+\color{orange}{\frac{-11}{14}}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(5)} + \color{orange}{(\frac{-11}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bp+5p-\frac{11}{14}b-\frac{11}{14}.5& \text{Uitwerken } \\ & =bp+5p-\frac{11}{14}b-\frac{55}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-2}{10})(q+\frac{-11}{6})& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{6}b+\frac{1}{5}q-\frac{1}{5}.\frac{11}{6}& \text{Uitwerken } \\ & =bq-\frac{11}{6}b+\frac{1}{5}q-\frac{11}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-8}{15})(\frac{13}{2}-p)& =(\color{red}{x}+\color{orange}{\frac{-8}{15}}).(\color{green}{-p}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{13}{2}x+\frac{8}{15}p-\frac{8}{15}.\frac{13}{2}& \text{Uitwerken } \\ & =-px+\frac{13}{2}x+\frac{8}{15}p-\frac{104}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{13}{2}x+\frac{8}{15}p-\frac{52}{15} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-10}{18}+x)(x-\frac{3}{9})& =(\color{red}{x}+\color{orange}{\frac{-5}{9}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{3}x-\frac{5}{9}x+\frac{5}{9}.\frac{1}{3}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{3})+(\frac{-5}{9}))x+\frac{5}{27} & \text{Neem samen} \\ &=x^2-\frac{8}{9}x+\frac{5}{27} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-19}{4}-x)(\frac{-9}{12}+a)& =(\color{red}{-x}+\color{orange}{\frac{-19}{4}}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-19}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{4})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{4}x-\frac{19}{4}a+\frac{19}{4}.\frac{3}{4}& \text{Uitwerken } \\ & =-ax+\frac{3}{4}x-\frac{19}{4}a+\frac{57}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{6}{16})(a+\frac{1}{15})& =(\color{red}{x}+\color{orange}{\frac{-3}{8}}).(\color{green}{a}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{15}x-\frac{3}{8}a-\frac{3}{8}.\frac{1}{15}& \text{Uitwerken } \\ & =ax+\frac{1}{15}x-\frac{3}{8}a-\frac{3}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{15}x-\frac{3}{8}a-\frac{1}{40} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-2}{20}+a)(q-\frac{1}{13})& =(\color{red}{a}+\color{orange}{\frac{-1}{10}}).(\color{green}{q}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{13}a-\frac{1}{10}q+\frac{1}{10}.\frac{1}{13}& \text{Uitwerken } \\ & =aq-\frac{1}{13}a-\frac{1}{10}q+\frac{1}{130} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{4}{2})(\frac{10}{4}+x)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{2}p+2x+2.\frac{5}{2}& \text{Uitwerken } \\ & =px+\frac{5}{2}p+2x+\frac{10}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{5}{2}p+2x+5 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{4}-b)(b+\frac{-2}{4})& =(\color{red}{-b}+\color{orange}{\frac{9}{4}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{9}{4})} . \color{green}{(b)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{2}b+\frac{9}{4}b-\frac{9}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{2}+\frac{9}{4})b-\frac{9}{8} & \text{Neem samen} \\ &=-b^2+\frac{11}{4}b-\frac{9}{8} & \text{Maak de som} \\\end{align}\)
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