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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-17)(x-\frac{-1}{9})& =(\color{red}{b}+\color{orange}{(-17)}).(\color{green}{x}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(-17)} . \color{green}{(x)} + \color{orange}{(-17)} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{9}b-17x-17.\frac{1}{9}& \text{Uitwerken } \\ & =bx+\frac{1}{9}b-17x-\frac{17}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-20}{13}-x)(\frac{2}{19}-b)& =(\color{red}{-x}+\color{orange}{\frac{-20}{13}}).(\color{green}{-b}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{19}x+\frac{20}{13}b-\frac{20}{13}.\frac{2}{19}& \text{Uitwerken } \\ & =bx-\frac{2}{19}x+\frac{20}{13}b-\frac{40}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{10}{13}+a)(p-\frac{12}{17})& =(\color{red}{a}+\color{orange}{\frac{10}{13}}).(\color{green}{p}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{10}{13})} . \color{green}{(p)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{12}{17}a+\frac{10}{13}p-\frac{10}{13}.\frac{12}{17}& \text{Uitwerken } \\ & =ap-\frac{12}{17}a+\frac{10}{13}p-\frac{120}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-14}{3}-b)(\frac{-3}{18}+a)& =(\color{red}{-b}+\color{orange}{\frac{-14}{3}}).(\color{green}{a}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{6}b-\frac{14}{3}a+\frac{14}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =-ab+\frac{1}{6}b-\frac{14}{3}a+\frac{14}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{1}{6}b-\frac{14}{3}a+\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{6}{17})(\frac{-5}{4}+b)& =(\color{red}{a}+\color{orange}{\frac{6}{17}}).(\color{green}{b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{6}{17})} . \color{green}{(b)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{4}a+\frac{6}{17}b-\frac{6}{17}.\frac{5}{4}& \text{Uitwerken } \\ & =ab-\frac{5}{4}a+\frac{6}{17}b-\frac{30}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{4}a+\frac{6}{17}b-\frac{15}{34} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-1}{13})(p-\frac{8}{15})& =(\color{red}{q}+\color{orange}{\frac{1}{13}}).(\color{green}{p}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(\frac{1}{13})} . \color{green}{(p)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{15}q+\frac{1}{13}p-\frac{1}{13}.\frac{8}{15}& \text{Uitwerken } \\ & =pq-\frac{8}{15}q+\frac{1}{13}p-\frac{8}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{6}{16}-x)(\frac{-14}{6}+q)& =(\color{red}{-x}+\color{orange}{\frac{3}{8}}).(\color{green}{q}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{7}{3}x+\frac{3}{8}q-\frac{3}{8}.\frac{7}{3}& \text{Uitwerken } \\ & =-qx+\frac{7}{3}x+\frac{3}{8}q-\frac{21}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{7}{3}x+\frac{3}{8}q-\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{17}+b)(a+\frac{-17}{16})& =(\color{red}{b}+\color{orange}{\frac{12}{17}}).(\color{green}{a}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{17}{16}b+\frac{12}{17}a-\frac{12}{17}.\frac{17}{16}& \text{Uitwerken } \\ & =ab-\frac{17}{16}b+\frac{12}{17}a-\frac{204}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{17}{16}b+\frac{12}{17}a-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{3}{9}-b)(\frac{16}{12}+x)& =(\color{red}{-b}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{3}b+\frac{1}{3}x+\frac{1}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =-bx-\frac{4}{3}b+\frac{1}{3}x+\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{15}{5})(\frac{9}{4}+q)& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{q}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(-3)} . \color{green}{(q)} + \color{orange}{(-3)} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{4}x-3q-3.\frac{9}{4}& \text{Uitwerken } \\ & =qx+\frac{9}{4}x-3q-\frac{27}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-1}{20})(a+\frac{-12}{11})& =(\color{red}{a}+\color{orange}{\frac{1}{20}}).(\color{green}{a}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(\frac{1}{20})} . \color{green}{(a)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{12}{11}a+\frac{1}{20}a-\frac{1}{20}.\frac{12}{11}& \text{Uitwerken } \\ & =a^2+((\frac{-12}{11})+\frac{1}{20})a-(\frac{-12}{220}) & \text{Neem samen} \\ &=a^2-\frac{229}{220}a-(\frac{-12}{220}) & \text{Maak de som} \\ &=a^2-\frac{229}{220}a+\frac{3}{55} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-17}{4})(b+12)& =(\color{red}{b}+\color{orange}{\frac{17}{4}}).(\color{green}{b}+\color{blue}{12})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(12)} + \color{orange}{(\frac{17}{4})} . \color{green}{(b)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = bb+12b+\frac{17}{4}b+\frac{17}{4}.12& \text{Uitwerken } \\ & =b^2+(12+\frac{17}{4})b+\frac{204}{4} & \text{Neem samen} \\ &=b^2+\frac{65}{4}b+\frac{204}{4} & \text{Maak de som} \\ &=b^2+\frac{65}{4}b+51 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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