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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-20}{8})(x+\frac{-6}{12})& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}b-\frac{5}{2}x+\frac{5}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}b-\frac{5}{2}x+\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}((-8)+a)(\frac{-1}{4}+q)& =(\color{red}{a}+\color{orange}{(-8)}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(-8)} . \color{green}{(q)} + \color{orange}{(-8)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{4}a-8q+8.\frac{1}{4}& \text{Uitwerken } \\ & =aq-\frac{1}{4}a-8q+\frac{8}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{4}a-8q+2 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{11}{15}+a)(\frac{13}{17}-a)& =(\color{red}{a}+\color{orange}{\frac{11}{15}}).(\color{green}{-a}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{11}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{13}{17}a-\frac{11}{15}a+\frac{11}{15}.\frac{13}{17}& \text{Uitwerken } \\ & =-a^2+(\frac{13}{17}+(\frac{-11}{15}))a+(\frac{-143}{255}) & \text{Neem samen} \\ &=-a^2+\frac{8}{255}a+(\frac{-143}{255}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{15}{12}+q)(\frac{-11}{13}-b)& =(\color{red}{q}+\color{orange}{\frac{5}{4}}).(\color{green}{-b}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{13}q-\frac{5}{4}b-\frac{5}{4}.\frac{11}{13}& \text{Uitwerken } \\ & =-bq-\frac{11}{13}q-\frac{5}{4}b-\frac{55}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-9}{2})(\frac{-4}{14}+x)& =(\color{red}{x}+\color{orange}{\frac{-9}{2}}).(\color{green}{x}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{2}{7}x-\frac{9}{2}x+\frac{9}{2}.\frac{2}{7}& \text{Uitwerken } \\ & =x^2+((\frac{-2}{7})+(\frac{-9}{2}))x+\frac{18}{14} & \text{Neem samen} \\ &=x^2-\frac{67}{14}x+\frac{18}{14} & \text{Maak de som} \\ &=x^2-\frac{67}{14}x+\frac{9}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-7}{19})(q+(-14))& =(\color{red}{p}+\color{orange}{\frac{7}{19}}).(\color{green}{q}+\color{blue}{(-14)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-14)} + \color{orange}{(\frac{7}{19})} . \color{green}{(q)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = pq-14p+\frac{7}{19}q-\frac{7}{19}.14& \text{Uitwerken } \\ & =pq-14p+\frac{7}{19}q-\frac{98}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{16}{16})(\frac{11}{4}+x)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{4}q+1x+1.\frac{11}{4}& \text{Uitwerken } \\ & =qx+\frac{11}{4}q+1x+\frac{11}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-6}{11}+p)(b-\frac{-12}{7})& =(\color{red}{p}+\color{orange}{\frac{-6}{11}}).(\color{green}{b}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{12}{7}p-\frac{6}{11}b-\frac{6}{11}.\frac{12}{7}& \text{Uitwerken } \\ & =bp+\frac{12}{7}p-\frac{6}{11}b-\frac{72}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{2}{4})((-10)+q)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{(-10)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-10)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = qq-10q-\frac{1}{2}q+\frac{1}{2}.10& \text{Uitwerken } \\ & =q^2+((-10)+(\frac{-1}{2}))q+\frac{10}{2} & \text{Neem samen} \\ &=q^2-\frac{21}{2}q+\frac{10}{2} & \text{Maak de som} \\ &=q^2-\frac{21}{2}q+5 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-3}{11}+x)(b-\frac{-18}{14})& =(\color{red}{x}+\color{orange}{\frac{-3}{11}}).(\color{green}{b}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{7}x-\frac{3}{11}b-\frac{3}{11}.\frac{9}{7}& \text{Uitwerken } \\ & =bx+\frac{9}{7}x-\frac{3}{11}b-\frac{27}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-14}{3})(\frac{-8}{16}-x)& =(\color{red}{p}+\color{orange}{\frac{-14}{3}}).(\color{green}{-x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{2}p+\frac{14}{3}x+\frac{14}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =-px-\frac{1}{2}p+\frac{14}{3}x+\frac{14}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{1}{2}p+\frac{14}{3}x+\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a-\frac{13}{20})(p-\frac{-11}{15})& =(\color{red}{a}+\color{orange}{\frac{-13}{20}}).(\color{green}{p}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{15}a-\frac{13}{20}p-\frac{13}{20}.\frac{11}{15}& \text{Uitwerken } \\ & =ap+\frac{11}{15}a-\frac{13}{20}p-\frac{143}{300} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-25 17:49:25
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