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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{6}-x)(b-\frac{-6}{4})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{2}x-1b-1.\frac{3}{2}& \text{Uitwerken } \\ & =-bx-\frac{3}{2}x-1b-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-6}{12}+a)(a+\frac{7}{19})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{19}a-\frac{1}{2}a-\frac{1}{2}.\frac{7}{19}& \text{Uitwerken } \\ & =a^2+(\frac{7}{19}+(\frac{-1}{2}))a-(\frac{-7}{38}) & \text{Neem samen} \\ &=a^2-\frac{5}{38}a-(\frac{-7}{38}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-4}{11}+b)(a+\frac{8}{11})& =(\color{red}{b}+\color{orange}{\frac{-4}{11}}).(\color{green}{a}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{11}b-\frac{4}{11}a-\frac{4}{11}.\frac{8}{11}& \text{Uitwerken } \\ & =ab+\frac{8}{11}b-\frac{4}{11}a-\frac{32}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{5}{4}+x)(\frac{16}{9}-x)& =(\color{red}{x}+\color{orange}{\frac{5}{4}}).(\color{green}{-x}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{16}{9}x-\frac{5}{4}x+\frac{5}{4}.\frac{16}{9}& \text{Uitwerken } \\ & =-x^2+(\frac{16}{9}+(\frac{-5}{4}))x+(\frac{-80}{36}) & \text{Neem samen} \\ &=-x^2+\frac{19}{36}x+(\frac{-80}{36}) & \text{Maak de som} \\ &=-x^2+\frac{19}{36}x+(\frac{-20}{9}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(p+\frac{18}{16})(\frac{-12}{11}-b)& =(\color{red}{p}+\color{orange}{\frac{9}{8}}).(\color{green}{-b}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(\frac{9}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{12}{11}p-\frac{9}{8}b-\frac{9}{8}.\frac{12}{11}& \text{Uitwerken } \\ & =-bp-\frac{12}{11}p-\frac{9}{8}b-\frac{108}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{12}{11}p-\frac{9}{8}b-\frac{27}{22} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{17}{16}-x)(\frac{16}{5}+q)& =(\color{red}{-x}+\color{orange}{\frac{17}{16}}).(\color{green}{q}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{17}{16})} . \color{green}{(q)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{16}{5}x+\frac{17}{16}q+\frac{17}{16}.\frac{16}{5}& \text{Uitwerken } \\ & =-qx-\frac{16}{5}x+\frac{17}{16}q+\frac{272}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{16}{5}x+\frac{17}{16}q+\frac{17}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-7}{7})(b-(-7))& =(\color{red}{a}+\color{orange}{1}).(\color{green}{b}+\color{blue}{7})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(7)} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = ab+7a+1b+1.7& \text{Uitwerken } \\ & =ab+7a+1b+7 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(4+q)(a-\frac{-10}{19})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{a}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{19}q+4a+4.\frac{10}{19}& \text{Uitwerken } \\ & =aq+\frac{10}{19}q+4a+\frac{40}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-14}{17})(\frac{15}{4}+q)& =(\color{red}{b}+\color{orange}{\frac{14}{17}}).(\color{green}{q}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{14}{17})} . \color{green}{(q)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{4}b+\frac{14}{17}q+\frac{14}{17}.\frac{15}{4}& \text{Uitwerken } \\ & =bq+\frac{15}{4}b+\frac{14}{17}q+\frac{210}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{15}{4}b+\frac{14}{17}q+\frac{105}{34} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{17}{13}+b)(\frac{9}{15}+a)& =(\color{red}{b}+\color{orange}{\frac{17}{13}}).(\color{green}{a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{17}{13})} . \color{green}{(a)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{5}b+\frac{17}{13}a+\frac{17}{13}.\frac{3}{5}& \text{Uitwerken } \\ & =ab+\frac{3}{5}b+\frac{17}{13}a+\frac{51}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{15}-b)(p+\frac{7}{4})& =(\color{red}{-b}+\color{orange}{\frac{-4}{5}}).(\color{green}{p}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{4}b-\frac{4}{5}p-\frac{4}{5}.\frac{7}{4}& \text{Uitwerken } \\ & =-bp-\frac{7}{4}b-\frac{4}{5}p-\frac{28}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{7}{4}b-\frac{4}{5}p-\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-8}{18}+x)(x+\frac{-17}{6})& =(\color{red}{x}+\color{orange}{\frac{-4}{9}}).(\color{green}{x}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{17}{6}x-\frac{4}{9}x+\frac{4}{9}.\frac{17}{6}& \text{Uitwerken } \\ & =x^2+((\frac{-17}{6})+(\frac{-4}{9}))x+\frac{68}{54} & \text{Neem samen} \\ &=x^2-\frac{59}{18}x+\frac{68}{54} & \text{Maak de som} \\ &=x^2-\frac{59}{18}x+\frac{34}{27} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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