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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-\frac{-1}{12})(\frac{17}{13}+a)& =(\color{red}{x}+\color{orange}{\frac{1}{12}}).(\color{green}{a}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{1}{12})} . \color{green}{(a)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{13}x+\frac{1}{12}a+\frac{1}{12}.\frac{17}{13}& \text{Uitwerken } \\ & =ax+\frac{17}{13}x+\frac{1}{12}a+\frac{17}{156} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{16}{2}-p)(\frac{18}{8}+p)& =(\color{red}{-p}+\color{orange}{8}).(\color{green}{p}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(8)} . \color{green}{(p)} + \color{orange}{(8)} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{9}{4}p+8p+8.\frac{9}{4}& \text{Uitwerken } \\ & =-p^2+((\frac{-9}{4})+8)p+(\frac{-72}{4}) & \text{Neem samen} \\ &=-p^2+\frac{23}{4}p+(\frac{-72}{4}) & \text{Maak de som} \\ &=-p^2+\frac{23}{4}p+(-18) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
3. \(\begin{align}(q-\frac{-18}{17})(b+\frac{14}{19})& =(\color{red}{q}+\color{orange}{\frac{18}{17}}).(\color{green}{b}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(\frac{18}{17})} . \color{green}{(b)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{14}{19}q+\frac{18}{17}b+\frac{18}{17}.\frac{14}{19}& \text{Uitwerken } \\ & =bq+\frac{14}{19}q+\frac{18}{17}b+\frac{252}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-9}{18}+p)(\frac{-11}{2}+q)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{2}p-\frac{1}{2}q+\frac{1}{2}.\frac{11}{2}& \text{Uitwerken } \\ & =pq-\frac{11}{2}p-\frac{1}{2}q+\frac{11}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-11}{15})(\frac{18}{12}+p)& =(\color{red}{p}+\color{orange}{\frac{-11}{15}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{3}{2}p-\frac{11}{15}p-\frac{11}{15}.\frac{3}{2}& \text{Uitwerken } \\ & =p^2+(\frac{3}{2}+(\frac{-11}{15}))p-(\frac{-33}{30}) & \text{Neem samen} \\ &=p^2+\frac{23}{30}p-(\frac{-33}{30}) & \text{Maak de som} \\ &=p^2+\frac{23}{30}p+\frac{11}{10} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
6. \(\begin{align}(\frac{-10}{17}-a)(\frac{15}{20}-b)& =(\color{red}{-a}+\color{orange}{\frac{-10}{17}}).(\color{green}{-b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{4}a+\frac{10}{17}b-\frac{10}{17}.\frac{3}{4}& \text{Uitwerken } \\ & =ab-\frac{3}{4}a+\frac{10}{17}b-\frac{30}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{3}{4}a+\frac{10}{17}b-\frac{15}{34} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q-\frac{-18}{4})(b+\frac{10}{18})& =(\color{red}{q}+\color{orange}{\frac{9}{2}}).(\color{green}{b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{9}{2})} . \color{green}{(b)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{9}q+\frac{9}{2}b+\frac{9}{2}.\frac{5}{9}& \text{Uitwerken } \\ & =bq+\frac{5}{9}q+\frac{9}{2}b+\frac{45}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{5}{9}q+\frac{9}{2}b+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{19}{6}+q)(x-\frac{2}{6})& =(\color{red}{q}+\color{orange}{\frac{19}{6}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{19}{6})} . \color{green}{(x)} + \color{orange}{(\frac{19}{6})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{3}q+\frac{19}{6}x-\frac{19}{6}.\frac{1}{3}& \text{Uitwerken } \\ & =qx-\frac{1}{3}q+\frac{19}{6}x-\frac{19}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-4}{20}+q)(\frac{-8}{16}-q)& =(\color{red}{q}+\color{orange}{\frac{-1}{5}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{2}q+\frac{1}{5}q+\frac{1}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{2})+\frac{1}{5})q+(\frac{-1}{10}) & \text{Neem samen} \\ &=-q^2-\frac{3}{10}q+(\frac{-1}{10}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{-7}{20}-q)(\frac{5}{15}+p)& =(\color{red}{-q}+\color{orange}{\frac{-7}{20}}).(\color{green}{p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{3}q-\frac{7}{20}p-\frac{7}{20}.\frac{1}{3}& \text{Uitwerken } \\ & =-pq-\frac{1}{3}q-\frac{7}{20}p-\frac{7}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{15}{3}+p)(a-\frac{15}{17})& =(\color{red}{p}+\color{orange}{5}).(\color{green}{a}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(5)} . \color{green}{(a)} + \color{orange}{(5)} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{17}p+5a-5.\frac{15}{17}& \text{Uitwerken } \\ & =ap-\frac{15}{17}p+5a-\frac{75}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{-10}{12})(\frac{-12}{10}-b)& =(\color{red}{q}+\color{orange}{\frac{5}{6}}).(\color{green}{-b}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{6}{5}q-\frac{5}{6}b-\frac{5}{6}.\frac{6}{5}& \text{Uitwerken } \\ & =-bq-\frac{6}{5}q-\frac{5}{6}b-\frac{30}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{6}{5}q-\frac{5}{6}b-1 & \text{Vereenvoudig} \\\end{align}\)