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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{10}{16}-b)(p+\frac{7}{16})& =(\color{red}{-b}+\color{orange}{\frac{5}{8}}).(\color{green}{p}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{16}b+\frac{5}{8}p+\frac{5}{8}.\frac{7}{16}& \text{Uitwerken } \\ & =-bp-\frac{7}{16}b+\frac{5}{8}p+\frac{35}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-14}{2}+a)(b+\frac{16}{18})& =(\color{red}{a}+\color{orange}{(-7)}).(\color{green}{b}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(-7)} . \color{green}{(b)} + \color{orange}{(-7)} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{9}a-7b-7.\frac{8}{9}& \text{Uitwerken } \\ & =ab+\frac{8}{9}a-7b-\frac{56}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{6}{2})(\frac{9}{3}+p)& =(\color{red}{p}+\color{orange}{3}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = pp+3p+3p+3.3& \text{Uitwerken } \\ & =p^2+(3+3)p+9 & \text{Neem samen} \\ &=p^2+6p+9 & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-12}{12}-b)(\frac{-13}{14}+x)& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{13}{14}b-1x+1.\frac{13}{14}& \text{Uitwerken } \\ & =-bx+\frac{13}{14}b-1x+\frac{13}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(3-a)(\frac{16}{6}-a)& =(\color{red}{-a}+\color{orange}{3}).(\color{green}{-a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(3)} . \color{green}{(-a)} + \color{orange}{(3)} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{8}{3}a-3a+3.\frac{8}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-8}{3})+(-3))a+\frac{24}{3} & \text{Neem samen} \\ &=a^2-\frac{17}{3}a+\frac{24}{3} & \text{Maak de som} \\ &=a^2-\frac{17}{3}a+8 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{18}{4}+q)(\frac{-12}{6}-b)& =(\color{red}{q}+\color{orange}{\frac{9}{2}}).(\color{green}{-b}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{9}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bq-2q-\frac{9}{2}b-\frac{9}{2}.2& \text{Uitwerken } \\ & =-bq-2q-\frac{9}{2}b-\frac{18}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-2q-\frac{9}{2}b-9 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-20}{18})(\frac{-10}{15}-p)& =(\color{red}{b}+\color{orange}{\frac{-10}{9}}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{2}{3}b+\frac{10}{9}p+\frac{10}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =-bp-\frac{2}{3}b+\frac{10}{9}p+\frac{20}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-5}{17})((-18)-a)& =(\color{red}{b}+\color{orange}{\frac{5}{17}}).(\color{green}{-a}+\color{blue}{(-18)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-18)} + \color{orange}{(\frac{5}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = -ab-18b-\frac{5}{17}a-\frac{5}{17}.18& \text{Uitwerken } \\ & =-ab-18b-\frac{5}{17}a-\frac{90}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{20}-q)(b+\frac{11}{2})& =(\color{red}{-q}+\color{orange}{\frac{3}{10}}).(\color{green}{b}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{3}{10})} . \color{green}{(b)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{2}q+\frac{3}{10}b+\frac{3}{10}.\frac{11}{2}& \text{Uitwerken } \\ & =-bq-\frac{11}{2}q+\frac{3}{10}b+\frac{33}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{4}{4})(q-\frac{-9}{16})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{16}p-1q-1.\frac{9}{16}& \text{Uitwerken } \\ & =pq+\frac{9}{16}p-1q-\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+11)(\frac{-12}{16}-q)& =(\color{red}{q}+\color{orange}{11}).(\color{green}{-q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(11)} . \color{green}{(-q)} + \color{orange}{(11)} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{3}{4}q-11q-11.\frac{3}{4}& \text{Uitwerken } \\ & =-q^2+((\frac{-3}{4})+(-11))q-\frac{33}{4} & \text{Neem samen} \\ &=-q^2-\frac{47}{4}q-\frac{33}{4} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{10}{9}+x)(\frac{9}{5}-p)& =(\color{red}{x}+\color{orange}{\frac{10}{9}}).(\color{green}{-p}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{10}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{9}{5}x-\frac{10}{9}p+\frac{10}{9}.\frac{9}{5}& \text{Uitwerken } \\ & =-px+\frac{9}{5}x-\frac{10}{9}p+\frac{90}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{9}{5}x-\frac{10}{9}p+2 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-17 13:46:56
Een site van Busleyden Atheneum Mechelen