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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-19}{4})(\frac{-7}{16}-x)& =(\color{red}{p}+\color{orange}{\frac{-19}{4}}).(\color{green}{-x}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(\frac{-19}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{4})} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{16}p+\frac{19}{4}x+\frac{19}{4}.\frac{7}{16}& \text{Uitwerken } \\ & =-px-\frac{7}{16}p+\frac{19}{4}x+\frac{133}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{6}{3}+b)(q+\frac{-19}{5})& =(\color{red}{b}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{5}b+2q-2.\frac{19}{5}& \text{Uitwerken } \\ & =bq-\frac{19}{5}b+2q-\frac{38}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{20}{4})(\frac{-2}{9}+p)& =(\color{red}{b}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{9}b+5p-5.\frac{2}{9}& \text{Uitwerken } \\ & =bp-\frac{2}{9}b+5p-\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{17}{11})(\frac{-18}{4}-p)& =(\color{red}{p}+\color{orange}{\frac{17}{11}}).(\color{green}{-p}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{17}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{9}{2}p-\frac{17}{11}p-\frac{17}{11}.\frac{9}{2}& \text{Uitwerken } \\ & =-p^2+((\frac{-9}{2})+(\frac{-17}{11}))p-\frac{153}{22} & \text{Neem samen} \\ &=-p^2-\frac{133}{22}p-\frac{153}{22} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-11}{11}+b)(a+\frac{11}{17})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{17}b-1a-1.\frac{11}{17}& \text{Uitwerken } \\ & =ab+\frac{11}{17}b-1a-\frac{11}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-8}{19})(\frac{10}{6}+p)& =(\color{red}{a}+\color{orange}{\frac{8}{19}}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{8}{19})} . \color{green}{(p)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{3}a+\frac{8}{19}p+\frac{8}{19}.\frac{5}{3}& \text{Uitwerken } \\ & =ap+\frac{5}{3}a+\frac{8}{19}p+\frac{40}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{15}{17}-x)(p+\frac{-1}{4})& =(\color{red}{-x}+\color{orange}{\frac{15}{17}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{15}{17})} . \color{green}{(p)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{4}x+\frac{15}{17}p-\frac{15}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =-px+\frac{1}{4}x+\frac{15}{17}p-\frac{15}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{13}{14}+x)(\frac{14}{17}-b)& =(\color{red}{x}+\color{orange}{\frac{13}{14}}).(\color{green}{-b}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{13}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{14}{17}x-\frac{13}{14}b+\frac{13}{14}.\frac{14}{17}& \text{Uitwerken } \\ & =-bx+\frac{14}{17}x-\frac{13}{14}b+\frac{182}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{14}{17}x-\frac{13}{14}b+\frac{13}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{14}{7})(b+\frac{-3}{16})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{16}p-2b+2.\frac{3}{16}& \text{Uitwerken } \\ & =bp-\frac{3}{16}p-2b+\frac{6}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{16}p-2b+\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{7}-x)(x-\frac{4}{14})& =(\color{red}{-x}+\color{orange}{\frac{3}{7}}).(\color{green}{x}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{2}{7}x+\frac{3}{7}x-\frac{3}{7}.\frac{2}{7}& \text{Uitwerken } \\ & =-x^2+(\frac{2}{7}+\frac{3}{7})x-\frac{6}{49} & \text{Neem samen} \\ &=-x^2+\frac{5}{7}x-\frac{6}{49} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{3}{2}-x)(x-13)& =(\color{red}{-x}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{(-13)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(-13)} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = -xx+13x+\frac{3}{2}x-\frac{3}{2}.13& \text{Uitwerken } \\ & =-x^2+(13+\frac{3}{2})x-\frac{39}{2} & \text{Neem samen} \\ &=-x^2+\frac{29}{2}x-\frac{39}{2} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(b-\frac{2}{8})(\frac{11}{20}-p)& =(\color{red}{b}+\color{orange}{\frac{-1}{4}}).(\color{green}{-p}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{11}{20}b+\frac{1}{4}p-\frac{1}{4}.\frac{11}{20}& \text{Uitwerken } \\ & =-bp+\frac{11}{20}b+\frac{1}{4}p-\frac{11}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-04 17:17:24
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