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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-8}{2}-b)(\frac{10}{5}-p)& =(\color{red}{-b}+\color{orange}{(-4)}).(\color{green}{-p}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(2)} + \color{orange}{(-4)} . \color{green}{(-p)} + \color{orange}{(-4)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bp-2b+4p-4.2& \text{Uitwerken } \\ & =bp-2b+4p-8 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{8}{6})(q+\frac{19}{19})& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1x-\frac{4}{3}q-\frac{4}{3}.1& \text{Uitwerken } \\ & =qx+1x-\frac{4}{3}q-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{10}{7})(b-\frac{-5}{11})& =(\color{red}{p}+\color{orange}{\frac{10}{7}}).(\color{green}{b}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(\frac{10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{11}p+\frac{10}{7}b+\frac{10}{7}.\frac{5}{11}& \text{Uitwerken } \\ & =bp+\frac{5}{11}p+\frac{10}{7}b+\frac{50}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-12}{6})(p+\frac{6}{2})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ap+3a+2p+2.3& \text{Uitwerken } \\ & =ap+3a+2p+6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-11}{13})(p-\frac{-17}{4})& =(\color{red}{a}+\color{orange}{\frac{11}{13}}).(\color{green}{p}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{4}a+\frac{11}{13}p+\frac{11}{13}.\frac{17}{4}& \text{Uitwerken } \\ & =ap+\frac{17}{4}a+\frac{11}{13}p+\frac{187}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{16}{16}-b)(a+\frac{-15}{15})& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab+1b+1a-1.1& \text{Uitwerken } \\ & =-ab+1b+1a-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-6}{4}+q)(a-\frac{16}{4})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aq-4q-\frac{3}{2}a+\frac{3}{2}.4& \text{Uitwerken } \\ & =aq-4q-\frac{3}{2}a+\frac{12}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-4q-\frac{3}{2}a+6 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{13}{16}-a)(x-(-12))& =(\color{red}{-a}+\color{orange}{\frac{13}{16}}).(\color{green}{x}+\color{blue}{12})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(12)} + \color{orange}{(\frac{13}{16})} . \color{green}{(x)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = -ax-12a+\frac{13}{16}x+\frac{13}{16}.12& \text{Uitwerken } \\ & =-ax-12a+\frac{13}{16}x+\frac{156}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-12a+\frac{13}{16}x+\frac{39}{4} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-17}{9}+p)(x+\frac{-15}{7})& =(\color{red}{p}+\color{orange}{\frac{-17}{9}}).(\color{green}{x}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{15}{7}p-\frac{17}{9}x+\frac{17}{9}.\frac{15}{7}& \text{Uitwerken } \\ & =px-\frac{15}{7}p-\frac{17}{9}x+\frac{255}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{15}{7}p-\frac{17}{9}x+\frac{85}{21} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{8}+a)(p-\frac{-7}{4})& =(\color{red}{a}+\color{orange}{\frac{9}{4}}).(\color{green}{p}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{4}a+\frac{9}{4}p+\frac{9}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =ap+\frac{7}{4}a+\frac{9}{4}p+\frac{63}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{10}{13})(q-\frac{-9}{3})& =(\color{red}{q}+\color{orange}{\frac{10}{13}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{10}{13})} . \color{green}{(q)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qq+3q+\frac{10}{13}q+\frac{10}{13}.3& \text{Uitwerken } \\ & =q^2+(3+\frac{10}{13})q+\frac{30}{13} & \text{Neem samen} \\ &=q^2+\frac{49}{13}q+\frac{30}{13} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q-\frac{19}{18})(\frac{18}{13}-p)& =(\color{red}{q}+\color{orange}{\frac{-19}{18}}).(\color{green}{-p}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{18}{13}q+\frac{19}{18}p-\frac{19}{18}.\frac{18}{13}& \text{Uitwerken } \\ & =-pq+\frac{18}{13}q+\frac{19}{18}p-\frac{342}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{18}{13}q+\frac{19}{18}p-\frac{19}{13} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-02 20:28:59
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