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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-3}{6})(\frac{6}{10}-p)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{-p}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{5}x-\frac{1}{2}p+\frac{1}{2}.\frac{3}{5}& \text{Uitwerken } \\ & =-px+\frac{3}{5}x-\frac{1}{2}p+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{5}{13})(x-\frac{-11}{16})& =(\color{red}{a}+\color{orange}{\frac{-5}{13}}).(\color{green}{x}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{16}a-\frac{5}{13}x-\frac{5}{13}.\frac{11}{16}& \text{Uitwerken } \\ & =ax+\frac{11}{16}a-\frac{5}{13}x-\frac{55}{208} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-14}{3})(a-\frac{-1}{3})& =(\color{red}{x}+\color{orange}{\frac{-14}{3}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{3}x-\frac{14}{3}a-\frac{14}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =ax+\frac{1}{3}x-\frac{14}{3}a-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-13}{6}+b)(q-\frac{6}{2})& =(\color{red}{b}+\color{orange}{\frac{-13}{6}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{-13}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bq-3b-\frac{13}{6}q+\frac{13}{6}.3& \text{Uitwerken } \\ & =bq-3b-\frac{13}{6}q+\frac{39}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-3b-\frac{13}{6}q+\frac{13}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p+20)(b+\frac{17}{17})& =(\color{red}{p}+\color{orange}{20}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(20)} . \color{green}{(b)} + \color{orange}{(20)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p+20b+20.1& \text{Uitwerken } \\ & =bp+1p+20b+20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{16}+p)(\frac{-9}{11}-q)& =(\color{red}{p}+\color{orange}{\frac{5}{4}}).(\color{green}{-q}+\color{blue}{\frac{-9}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{11})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-9}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{11}p-\frac{5}{4}q-\frac{5}{4}.\frac{9}{11}& \text{Uitwerken } \\ & =-pq-\frac{9}{11}p-\frac{5}{4}q-\frac{45}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-11}{11}-b)(q-\frac{-9}{14})& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{14}b-1q-1.\frac{9}{14}& \text{Uitwerken } \\ & =-bq-\frac{9}{14}b-1q-\frac{9}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{8}{18})(\frac{-12}{20}-q)& =(\color{red}{a}+\color{orange}{\frac{4}{9}}).(\color{green}{-q}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{4}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{5}a-\frac{4}{9}q-\frac{4}{9}.\frac{3}{5}& \text{Uitwerken } \\ & =-aq-\frac{3}{5}a-\frac{4}{9}q-\frac{12}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{3}{5}a-\frac{4}{9}q-\frac{4}{15} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-20}{17}+x)(b-\frac{19}{11})& =(\color{red}{x}+\color{orange}{\frac{-20}{17}}).(\color{green}{b}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{11}x-\frac{20}{17}b+\frac{20}{17}.\frac{19}{11}& \text{Uitwerken } \\ & =bx-\frac{19}{11}x-\frac{20}{17}b+\frac{380}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{2}{8})(\frac{-3}{20}+a)& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{a}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{20}a-\frac{1}{4}a+\frac{1}{4}.\frac{3}{20}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{20})+(\frac{-1}{4}))a+\frac{3}{80} & \text{Neem samen} \\ &=a^2-\frac{8}{20}a+\frac{3}{80} & \text{Maak de som} \\ &=a^2-\frac{2}{5}a+\frac{3}{80} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-8}{4}-a)(\frac{-9}{18}+a)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{2}a-2a+2.\frac{1}{2}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{2}+(-2))a+(\frac{-2}{2}) & \text{Neem samen} \\ &=-a^2-\frac{3}{2}a+(\frac{-2}{2}) & \text{Maak de som} \\ &=-a^2-\frac{3}{2}a+(-1) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(a+\frac{11}{20})(\frac{-14}{13}-p)& =(\color{red}{a}+\color{orange}{\frac{11}{20}}).(\color{green}{-p}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{11}{20})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{14}{13}a-\frac{11}{20}p-\frac{11}{20}.\frac{14}{13}& \text{Uitwerken } \\ & =-ap-\frac{14}{13}a-\frac{11}{20}p-\frac{154}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{14}{13}a-\frac{11}{20}p-\frac{77}{130} & \text{Vereenvoudig} \\\end{align}\)
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