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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{14}{2})(x-\frac{-20}{16})& =(\color{red}{x}+\color{orange}{7}).(\color{green}{x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(7)} . \color{green}{(x)} + \color{orange}{(7)} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{5}{4}x+7x+7.\frac{5}{4}& \text{Uitwerken } \\ & =x^2+(\frac{5}{4}+7)x+\frac{35}{4} & \text{Neem samen} \\ &=x^2+\frac{33}{4}x+\frac{35}{4} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-13}{19}-a)(a+\frac{-20}{18})& =(\color{red}{-a}+\color{orange}{\frac{-13}{19}}).(\color{green}{a}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{10}{9}a-\frac{13}{19}a+\frac{13}{19}.\frac{10}{9}& \text{Uitwerken } \\ & =-a^2+(\frac{10}{9}+(\frac{-13}{19}))a+(\frac{-130}{171}) & \text{Neem samen} \\ &=-a^2+\frac{73}{171}a+(\frac{-130}{171}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{19}+a)(\frac{11}{15}-q)& =(\color{red}{a}+\color{orange}{\frac{6}{19}}).(\color{green}{-q}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{6}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{11}{15}a-\frac{6}{19}q+\frac{6}{19}.\frac{11}{15}& \text{Uitwerken } \\ & =-aq+\frac{11}{15}a-\frac{6}{19}q+\frac{66}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{11}{15}a-\frac{6}{19}q+\frac{22}{95} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-13}{10}+b)(\frac{13}{20}-x)& =(\color{red}{b}+\color{orange}{\frac{-13}{10}}).(\color{green}{-x}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{13}{20}b+\frac{13}{10}x-\frac{13}{10}.\frac{13}{20}& \text{Uitwerken } \\ & =-bx+\frac{13}{20}b+\frac{13}{10}x-\frac{169}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(3-q)(\frac{-11}{9}-p)& =(\color{red}{-q}+\color{orange}{3}).(\color{green}{-p}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(3)} . \color{green}{(-p)} + \color{orange}{(3)} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{9}q-3p-3.\frac{11}{9}& \text{Uitwerken } \\ & =pq+\frac{11}{9}q-3p-\frac{33}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{11}{9}q-3p-\frac{11}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{9}-b)(\frac{14}{12}-b)& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{7}{6}b+1b-1.\frac{7}{6}& \text{Uitwerken } \\ & =b^2+((\frac{-7}{6})+1)b-(\frac{-7}{6}) & \text{Neem samen} \\ &=b^2-\frac{1}{6}b-(\frac{-7}{6}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-2}{10})(\frac{-17}{17}-p)& =(\color{red}{p}+\color{orange}{\frac{1}{5}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pp-1p-\frac{1}{5}p-\frac{1}{5}.1& \text{Uitwerken } \\ & =-p^2+((-1)+(\frac{-1}{5}))p-\frac{1}{5} & \text{Neem samen} \\ &=-p^2-\frac{6}{5}p-\frac{1}{5} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-10}{3}+a)(a-\frac{-7}{13})& =(\color{red}{a}+\color{orange}{\frac{-10}{3}}).(\color{green}{a}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{13}a-\frac{10}{3}a-\frac{10}{3}.\frac{7}{13}& \text{Uitwerken } \\ & =a^2+(\frac{7}{13}+(\frac{-10}{3}))a-(\frac{-70}{39}) & \text{Neem samen} \\ &=a^2-\frac{109}{39}a-(\frac{-70}{39}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{1}{12}-b)(\frac{-10}{17}-p)& =(\color{red}{-b}+\color{orange}{\frac{1}{12}}).(\color{green}{-p}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{1}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{10}{17}b-\frac{1}{12}p-\frac{1}{12}.\frac{10}{17}& \text{Uitwerken } \\ & =bp+\frac{10}{17}b-\frac{1}{12}p-\frac{10}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{10}{17}b-\frac{1}{12}p-\frac{5}{102} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x+\frac{13}{11})(\frac{-12}{19}+q)& =(\color{red}{x}+\color{orange}{\frac{13}{11}}).(\color{green}{q}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{13}{11})} . \color{green}{(q)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{12}{19}x+\frac{13}{11}q-\frac{13}{11}.\frac{12}{19}& \text{Uitwerken } \\ & =qx-\frac{12}{19}x+\frac{13}{11}q-\frac{156}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{10}+b)(q-\frac{-12}{16})& =(\color{red}{b}+\color{orange}{\frac{-6}{5}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{4}b-\frac{6}{5}q-\frac{6}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =bq+\frac{3}{4}b-\frac{6}{5}q-\frac{18}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{3}{4}b-\frac{6}{5}q-\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-6}{20})(p+\frac{16}{20})& =(\color{red}{q}+\color{orange}{\frac{3}{10}}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{5}q+\frac{3}{10}p+\frac{3}{10}.\frac{4}{5}& \text{Uitwerken } \\ & =pq+\frac{4}{5}q+\frac{3}{10}p+\frac{12}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{4}{5}q+\frac{3}{10}p+\frac{6}{25} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-30 01:07:17
Een site van Busleyden Atheneum Mechelen