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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{-14}{12})(\frac{-19}{6}-x)& =(\color{red}{q}+\color{orange}{\frac{-7}{6}}).(\color{green}{-x}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{6}q+\frac{7}{6}x+\frac{7}{6}.\frac{19}{6}& \text{Uitwerken } \\ & =-qx-\frac{19}{6}q+\frac{7}{6}x+\frac{133}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-12)(q-\frac{-5}{17})& =(\color{red}{q}+\color{orange}{(-12)}).(\color{green}{q}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(-12)} . \color{green}{(q)} + \color{orange}{(-12)} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{17}q-12q-12.\frac{5}{17}& \text{Uitwerken } \\ & =q^2+(\frac{5}{17}+(-12))q-(\frac{-60}{17}) & \text{Neem samen} \\ &=q^2-\frac{199}{17}q-(\frac{-60}{17}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{13}{19}-p)(\frac{-13}{6}-x)& =(\color{red}{-p}+\color{orange}{\frac{13}{19}}).(\color{green}{-x}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{13}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{6}p-\frac{13}{19}x-\frac{13}{19}.\frac{13}{6}& \text{Uitwerken } \\ & =px+\frac{13}{6}p-\frac{13}{19}x-\frac{169}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q+(-8))(a-\frac{-8}{5})& =(\color{red}{q}+\color{orange}{(-8)}).(\color{green}{a}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(-8)} . \color{green}{(a)} + \color{orange}{(-8)} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{5}q-8a-8.\frac{8}{5}& \text{Uitwerken } \\ & =aq+\frac{8}{5}q-8a-\frac{64}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x+\frac{6}{7})(\frac{-8}{10}+x)& =(\color{red}{x}+\color{orange}{\frac{6}{7}}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{6}{7})} . \color{green}{(x)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{4}{5}x+\frac{6}{7}x-\frac{6}{7}.\frac{4}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-4}{5})+\frac{6}{7})x-(\frac{-24}{35}) & \text{Neem samen} \\ &=x^2+\frac{2}{35}x-(\frac{-24}{35}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-4}{16}-b)(\frac{-8}{19}-a)& =(\color{red}{-b}+\color{orange}{\frac{-1}{4}}).(\color{green}{-a}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{19}b+\frac{1}{4}a+\frac{1}{4}.\frac{8}{19}& \text{Uitwerken } \\ & =ab+\frac{8}{19}b+\frac{1}{4}a+\frac{8}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{8}{19}b+\frac{1}{4}a+\frac{2}{19} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(p+\frac{7}{19})(q+\frac{-4}{15})& =(\color{red}{p}+\color{orange}{\frac{7}{19}}).(\color{green}{q}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{7}{19})} . \color{green}{(q)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{15}p+\frac{7}{19}q-\frac{7}{19}.\frac{4}{15}& \text{Uitwerken } \\ & =pq-\frac{4}{15}p+\frac{7}{19}q-\frac{28}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x+\frac{-4}{11})(\frac{1}{11}-b)& =(\color{red}{x}+\color{orange}{\frac{-4}{11}}).(\color{green}{-b}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{11}x+\frac{4}{11}b-\frac{4}{11}.\frac{1}{11}& \text{Uitwerken } \\ & =-bx+\frac{1}{11}x+\frac{4}{11}b-\frac{4}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{19}{15})(x+\frac{-16}{9})& =(\color{red}{a}+\color{orange}{\frac{-19}{15}}).(\color{green}{x}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{16}{9}a-\frac{19}{15}x+\frac{19}{15}.\frac{16}{9}& \text{Uitwerken } \\ & =ax-\frac{16}{9}a-\frac{19}{15}x+\frac{304}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{18}{13})(\frac{5}{4}-q)& =(\color{red}{a}+\color{orange}{\frac{18}{13}}).(\color{green}{-q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{18}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{4}a-\frac{18}{13}q+\frac{18}{13}.\frac{5}{4}& \text{Uitwerken } \\ & =-aq+\frac{5}{4}a-\frac{18}{13}q+\frac{90}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{5}{4}a-\frac{18}{13}q+\frac{45}{26} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b-\frac{13}{18})(p+\frac{3}{11})& =(\color{red}{b}+\color{orange}{\frac{-13}{18}}).(\color{green}{p}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{11}b-\frac{13}{18}p-\frac{13}{18}.\frac{3}{11}& \text{Uitwerken } \\ & =bp+\frac{3}{11}b-\frac{13}{18}p-\frac{39}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{3}{11}b-\frac{13}{18}p-\frac{13}{66} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-14}{17}-q)(b+\frac{16}{19})& =(\color{red}{-q}+\color{orange}{\frac{-14}{17}}).(\color{green}{b}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{16}{19}q-\frac{14}{17}b-\frac{14}{17}.\frac{16}{19}& \text{Uitwerken } \\ & =-bq-\frac{16}{19}q-\frac{14}{17}b-\frac{224}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)