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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-1}{3})(\frac{13}{7}-q)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{-q}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{7}x-\frac{1}{3}q+\frac{1}{3}.\frac{13}{7}& \text{Uitwerken } \\ & =-qx+\frac{13}{7}x-\frac{1}{3}q+\frac{13}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{6}{13})(q+\frac{5}{18})& =(\color{red}{p}+\color{orange}{\frac{-6}{13}}).(\color{green}{q}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{18}p-\frac{6}{13}q-\frac{6}{13}.\frac{5}{18}& \text{Uitwerken } \\ & =pq+\frac{5}{18}p-\frac{6}{13}q-\frac{30}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{18}p-\frac{6}{13}q-\frac{5}{39} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-8}{4}-p)(q+\frac{-1}{8})& =(\color{red}{-p}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{8}p-2q+2.\frac{1}{8}& \text{Uitwerken } \\ & =-pq+\frac{1}{8}p-2q+\frac{2}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{1}{8}p-2q+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-6}{16})(x+\frac{-7}{12})& =(\color{red}{q}+\color{orange}{\frac{-3}{8}}).(\color{green}{x}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{12}q-\frac{3}{8}x+\frac{3}{8}.\frac{7}{12}& \text{Uitwerken } \\ & =qx-\frac{7}{12}q-\frac{3}{8}x+\frac{21}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{7}{12}q-\frac{3}{8}x+\frac{7}{32} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-12}{4}+b)(q-\frac{2}{17})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{q}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(-3)} . \color{green}{(q)} + \color{orange}{(-3)} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{17}b-3q+3.\frac{2}{17}& \text{Uitwerken } \\ & =bq-\frac{2}{17}b-3q+\frac{6}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-16}{2})(\frac{17}{5}-p)& =(\color{red}{p}+\color{orange}{8}).(\color{green}{-p}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(8)} . \color{green}{(-p)} + \color{orange}{(8)} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{17}{5}p-8p+8.\frac{17}{5}& \text{Uitwerken } \\ & =-p^2+(\frac{17}{5}+(-8))p+(\frac{-136}{5}) & \text{Neem samen} \\ &=-p^2-\frac{23}{5}p+(\frac{-136}{5}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-12}{14}-b)(p+\frac{11}{17})& =(\color{red}{-b}+\color{orange}{\frac{-6}{7}}).(\color{green}{p}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{11}{17}b-\frac{6}{7}p-\frac{6}{7}.\frac{11}{17}& \text{Uitwerken } \\ & =-bp-\frac{11}{17}b-\frac{6}{7}p-\frac{66}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{2}{18})(x+\frac{-15}{13})& =(\color{red}{b}+\color{orange}{\frac{-1}{9}}).(\color{green}{x}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{15}{13}b-\frac{1}{9}x+\frac{1}{9}.\frac{15}{13}& \text{Uitwerken } \\ & =bx-\frac{15}{13}b-\frac{1}{9}x+\frac{15}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{15}{13}b-\frac{1}{9}x+\frac{5}{39} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-7}{9})(a+\frac{-11}{5})& =(\color{red}{p}+\color{orange}{\frac{7}{9}}).(\color{green}{a}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(\frac{7}{9})} . \color{green}{(a)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{5}p+\frac{7}{9}a-\frac{7}{9}.\frac{11}{5}& \text{Uitwerken } \\ & =ap-\frac{11}{5}p+\frac{7}{9}a-\frac{77}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{13}+x)(x-\frac{8}{9})& =(\color{red}{x}+\color{orange}{\frac{10}{13}}).(\color{green}{x}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{10}{13})} . \color{green}{(x)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{8}{9}x+\frac{10}{13}x-\frac{10}{13}.\frac{8}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-8}{9})+\frac{10}{13})x-(\frac{-80}{117}) & \text{Neem samen} \\ &=x^2-\frac{14}{117}x-(\frac{-80}{117}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-14}{17})(\frac{1}{16}+x)& =(\color{red}{p}+\color{orange}{\frac{14}{17}}).(\color{green}{x}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{14}{17})} . \color{green}{(x)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{16}p+\frac{14}{17}x+\frac{14}{17}.\frac{1}{16}& \text{Uitwerken } \\ & =px+\frac{1}{16}p+\frac{14}{17}x+\frac{14}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{16}p+\frac{14}{17}x+\frac{7}{136} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-13}{7}-b)(p-\frac{-1}{20})& =(\color{red}{-b}+\color{orange}{\frac{-13}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{20}b-\frac{13}{7}p-\frac{13}{7}.\frac{1}{20}& \text{Uitwerken } \\ & =-bp-\frac{1}{20}b-\frac{13}{7}p-\frac{13}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-10 04:20:25
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