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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-14}{5})(\frac{6}{18}+q)& =(\color{red}{p}+\color{orange}{\frac{14}{5}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{14}{5})} . \color{green}{(q)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{3}p+\frac{14}{5}q+\frac{14}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =pq+\frac{1}{3}p+\frac{14}{5}q+\frac{14}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{11}{15})(\frac{-4}{8}-x)& =(\color{red}{p}+\color{orange}{\frac{-11}{15}}).(\color{green}{-x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{2}p+\frac{11}{15}x+\frac{11}{15}.\frac{1}{2}& \text{Uitwerken } \\ & =-px-\frac{1}{2}p+\frac{11}{15}x+\frac{11}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{4}-a)(\frac{14}{5}+p)& =(\color{red}{-a}+\color{orange}{\frac{-9}{2}}).(\color{green}{p}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{14}{5}a-\frac{9}{2}p-\frac{9}{2}.\frac{14}{5}& \text{Uitwerken } \\ & =-ap-\frac{14}{5}a-\frac{9}{2}p-\frac{126}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{14}{5}a-\frac{9}{2}p-\frac{63}{5} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-(-2))(\frac{1}{18}+x)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{18}q+2x+2.\frac{1}{18}& \text{Uitwerken } \\ & =qx+\frac{1}{18}q+2x+\frac{2}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{18}q+2x+\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p+\frac{-7}{17})(a-\frac{19}{11})& =(\color{red}{p}+\color{orange}{\frac{-7}{17}}).(\color{green}{a}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{11}p-\frac{7}{17}a+\frac{7}{17}.\frac{19}{11}& \text{Uitwerken } \\ & =ap-\frac{19}{11}p-\frac{7}{17}a+\frac{133}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(16-q)(q+\frac{-20}{19})& =(\color{red}{-q}+\color{orange}{16}).(\color{green}{q}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(16)} . \color{green}{(q)} + \color{orange}{(16)} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{20}{19}q+16q-16.\frac{20}{19}& \text{Uitwerken } \\ & =-q^2+(\frac{20}{19}+16)q-\frac{320}{19} & \text{Neem samen} \\ &=-q^2+\frac{324}{19}q-\frac{320}{19} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-9}{3})(p-\frac{-20}{3})& =(\color{red}{x}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{20}{3}x+3p+3.\frac{20}{3}& \text{Uitwerken } \\ & =px+\frac{20}{3}x+3p+\frac{60}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{20}{3}x+3p+20 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{2}{2})(a-\frac{-3}{18})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{6}p-1a-1.\frac{1}{6}& \text{Uitwerken } \\ & =ap+\frac{1}{6}p-1a-\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{3}{11}+p)(\frac{-3}{14}-a)& =(\color{red}{p}+\color{orange}{\frac{3}{11}}).(\color{green}{-a}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{3}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{14}p-\frac{3}{11}a-\frac{3}{11}.\frac{3}{14}& \text{Uitwerken } \\ & =-ap-\frac{3}{14}p-\frac{3}{11}a-\frac{9}{154} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{10}{18})(\frac{-10}{3}-b)& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{-b}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{10}{3}b+\frac{5}{9}b+\frac{5}{9}.\frac{10}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-10}{3})+\frac{5}{9})b+(\frac{-50}{27}) & \text{Neem samen} \\ &=-b^2-\frac{25}{9}b+(\frac{-50}{27}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(b+\frac{10}{7})(\frac{2}{8}+p)& =(\color{red}{b}+\color{orange}{\frac{10}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{4}b+\frac{10}{7}p+\frac{10}{7}.\frac{1}{4}& \text{Uitwerken } \\ & =bp+\frac{1}{4}b+\frac{10}{7}p+\frac{10}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{1}{4}b+\frac{10}{7}p+\frac{5}{14} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{16}-b)(p-\frac{-13}{13})& =(\color{red}{-b}+\color{orange}{\frac{9}{16}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{9}{16})} . \color{green}{(p)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1b+\frac{9}{16}p+\frac{9}{16}.1& \text{Uitwerken } \\ & =-bp-1b+\frac{9}{16}p+\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-27 10:07:45
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