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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-7}{3}-b)(\frac{18}{7}+p)& =(\color{red}{-b}+\color{orange}{\frac{-7}{3}}).(\color{green}{p}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{18}{7}b-\frac{7}{3}p-\frac{7}{3}.\frac{18}{7}& \text{Uitwerken } \\ & =-bp-\frac{18}{7}b-\frac{7}{3}p-\frac{126}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{18}{7}b-\frac{7}{3}p-6 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-4}{3})(\frac{1}{15}-a)& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{-a}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{15}b+\frac{4}{3}a-\frac{4}{3}.\frac{1}{15}& \text{Uitwerken } \\ & =-ab+\frac{1}{15}b+\frac{4}{3}a-\frac{4}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{12}{10}-b)(a+\frac{-17}{17})& =(\color{red}{-b}+\color{orange}{\frac{6}{5}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(\frac{6}{5})} . \color{green}{(a)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab+1b+\frac{6}{5}a-\frac{6}{5}.1& \text{Uitwerken } \\ & =-ab+1b+\frac{6}{5}a-\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{20}{10})(\frac{6}{8}+p)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{4}b+2p+2.\frac{3}{4}& \text{Uitwerken } \\ & =bp+\frac{3}{4}b+2p+\frac{6}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{3}{4}b+2p+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{19}{8}-a)(\frac{-12}{20}+q)& =(\color{red}{-a}+\color{orange}{\frac{19}{8}}).(\color{green}{q}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{19}{8})} . \color{green}{(q)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{5}a+\frac{19}{8}q-\frac{19}{8}.\frac{3}{5}& \text{Uitwerken } \\ & =-aq+\frac{3}{5}a+\frac{19}{8}q-\frac{57}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{5}+b)(a+\frac{4}{2})& =(\color{red}{b}+\color{orange}{\frac{-7}{5}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{-7}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ab+2b-\frac{7}{5}a-\frac{7}{5}.2& \text{Uitwerken } \\ & =ab+2b-\frac{7}{5}a-\frac{14}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-3}{17}+a)(\frac{-1}{20}+b)& =(\color{red}{a}+\color{orange}{\frac{-3}{17}}).(\color{green}{b}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-3}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{20}a-\frac{3}{17}b+\frac{3}{17}.\frac{1}{20}& \text{Uitwerken } \\ & =ab-\frac{1}{20}a-\frac{3}{17}b+\frac{3}{340} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{20}+x)(b-\frac{20}{16})& =(\color{red}{x}+\color{orange}{\frac{11}{20}}).(\color{green}{b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{11}{20})} . \color{green}{(b)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{4}x+\frac{11}{20}b-\frac{11}{20}.\frac{5}{4}& \text{Uitwerken } \\ & =bx-\frac{5}{4}x+\frac{11}{20}b-\frac{55}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{5}{4}x+\frac{11}{20}b-\frac{11}{16} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{14}{19}-p)(p+\frac{19}{15})& =(\color{red}{-p}+\color{orange}{\frac{14}{19}}).(\color{green}{p}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{14}{19})} . \color{green}{(p)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{19}{15}p+\frac{14}{19}p+\frac{14}{19}.\frac{19}{15}& \text{Uitwerken } \\ & =-p^2+((\frac{-19}{15})+\frac{14}{19})p+(\frac{-266}{285}) & \text{Neem samen} \\ &=-p^2-\frac{151}{285}p+(\frac{-266}{285}) & \text{Maak de som} \\ &=-p^2-\frac{151}{285}p+(\frac{-14}{15}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(p-\frac{2}{12})(x+\frac{10}{15})& =(\color{red}{p}+\color{orange}{\frac{-1}{6}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{2}{3}p-\frac{1}{6}x-\frac{1}{6}.\frac{2}{3}& \text{Uitwerken } \\ & =px+\frac{2}{3}p-\frac{1}{6}x-\frac{2}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{2}{3}p-\frac{1}{6}x-\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-5}{4})(\frac{-2}{5}-p)& =(\color{red}{x}+\color{orange}{\frac{5}{4}}).(\color{green}{-p}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{5}x-\frac{5}{4}p-\frac{5}{4}.\frac{2}{5}& \text{Uitwerken } \\ & =-px-\frac{2}{5}x-\frac{5}{4}p-\frac{10}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{2}{5}x-\frac{5}{4}p-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{10}+x)(\frac{-8}{7}-a)& =(\color{red}{x}+\color{orange}{\frac{13}{10}}).(\color{green}{-a}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{13}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{8}{7}x-\frac{13}{10}a-\frac{13}{10}.\frac{8}{7}& \text{Uitwerken } \\ & =-ax-\frac{8}{7}x-\frac{13}{10}a-\frac{104}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{8}{7}x-\frac{13}{10}a-\frac{52}{35} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-11 09:17:29
Een site van Busleyden Atheneum Mechelen