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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{15}+b)(p-\frac{19}{4})& =(\color{red}{b}+\color{orange}{\frac{7}{15}}).(\color{green}{p}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{7}{15})} . \color{green}{(p)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{4}b+\frac{7}{15}p-\frac{7}{15}.\frac{19}{4}& \text{Uitwerken } \\ & =bp-\frac{19}{4}b+\frac{7}{15}p-\frac{133}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{9}+p)(\frac{-19}{18}+a)& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{18}p+\frac{5}{3}a-\frac{5}{3}.\frac{19}{18}& \text{Uitwerken } \\ & =ap-\frac{19}{18}p+\frac{5}{3}a-\frac{95}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-10}{20})(a+8)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{8})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(8)} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = ax+8x+\frac{1}{2}a+\frac{1}{2}.8& \text{Uitwerken } \\ & =ax+8x+\frac{1}{2}a+\frac{8}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+8x+\frac{1}{2}a+4 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{18}{4}+q)(16+q)& =(\color{red}{q}+\color{orange}{\frac{9}{2}}).(\color{green}{q}+\color{blue}{16})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(16)} + \color{orange}{(\frac{9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = qq+16q+\frac{9}{2}q+\frac{9}{2}.16& \text{Uitwerken } \\ & =q^2+(16+\frac{9}{2})q+\frac{144}{2} & \text{Neem samen} \\ &=q^2+\frac{41}{2}q+\frac{144}{2} & \text{Maak de som} \\ &=q^2+\frac{41}{2}q+72 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{19}+b)(\frac{-20}{11}-q)& =(\color{red}{b}+\color{orange}{\frac{-6}{19}}).(\color{green}{-q}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{-6}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{20}{11}b+\frac{6}{19}q+\frac{6}{19}.\frac{20}{11}& \text{Uitwerken } \\ & =-bq-\frac{20}{11}b+\frac{6}{19}q+\frac{120}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-8}{2})(x-\frac{-3}{16})& =(\color{red}{b}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{16}b+4x+4.\frac{3}{16}& \text{Uitwerken } \\ & =bx+\frac{3}{16}b+4x+\frac{12}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{16}b+4x+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-19}{4}-x)(b-\frac{17}{2})& =(\color{red}{-x}+\color{orange}{\frac{-19}{4}}).(\color{green}{b}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{-19}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{4})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{17}{2}x-\frac{19}{4}b+\frac{19}{4}.\frac{17}{2}& \text{Uitwerken } \\ & =-bx+\frac{17}{2}x-\frac{19}{4}b+\frac{323}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-14}{12})(\frac{-1}{12}-b)& =(\color{red}{q}+\color{orange}{\frac{-7}{6}}).(\color{green}{-b}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{12}q+\frac{7}{6}b+\frac{7}{6}.\frac{1}{12}& \text{Uitwerken } \\ & =-bq-\frac{1}{12}q+\frac{7}{6}b+\frac{7}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-13}{18})(p-3)& =(\color{red}{p}+\color{orange}{\frac{13}{18}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{13}{18})} . \color{green}{(p)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pp-3p+\frac{13}{18}p-\frac{13}{18}.3& \text{Uitwerken } \\ & =p^2+((-3)+\frac{13}{18})p-(\frac{-39}{18}) & \text{Neem samen} \\ &=p^2-\frac{41}{18}p-(\frac{-39}{18}) & \text{Maak de som} \\ &=p^2-\frac{41}{18}p+\frac{13}{6} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{13}+p)(\frac{-8}{11}+p)& =(\color{red}{p}+\color{orange}{\frac{-9}{13}}).(\color{green}{p}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{8}{11}p-\frac{9}{13}p+\frac{9}{13}.\frac{8}{11}& \text{Uitwerken } \\ & =p^2+((\frac{-8}{11})+(\frac{-9}{13}))p+\frac{72}{143} & \text{Neem samen} \\ &=p^2-\frac{203}{143}p+\frac{72}{143} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{7}-x)(a-\frac{8}{15})& =(\color{red}{-x}+\color{orange}{\frac{-3}{7}}).(\color{green}{a}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{8}{15}x-\frac{3}{7}a+\frac{3}{7}.\frac{8}{15}& \text{Uitwerken } \\ & =-ax+\frac{8}{15}x-\frac{3}{7}a+\frac{24}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{8}{15}x-\frac{3}{7}a+\frac{8}{35} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{18}{2}-q)(x+\frac{-17}{13})& =(\color{red}{-q}+\color{orange}{9}).(\color{green}{x}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(9)} . \color{green}{(x)} + \color{orange}{(9)} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{17}{13}q+9x-9.\frac{17}{13}& \text{Uitwerken } \\ & =-qx+\frac{17}{13}q+9x-\frac{153}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-15 10:54:13
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