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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-10}{9})(\frac{-19}{11}-b)& =(\color{red}{p}+\color{orange}{\frac{-10}{9}}).(\color{green}{-b}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{11}p+\frac{10}{9}b+\frac{10}{9}.\frac{19}{11}& \text{Uitwerken } \\ & =-bp-\frac{19}{11}p+\frac{10}{9}b+\frac{190}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{5}{8})(\frac{-18}{9}-q)& =(\color{red}{x}+\color{orange}{\frac{5}{8}}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{5}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -qx-2x-\frac{5}{8}q-\frac{5}{8}.2& \text{Uitwerken } \\ & =-qx-2x-\frac{5}{8}q-\frac{10}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-2x-\frac{5}{8}q-\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{1}{2}+q)(p+\frac{-8}{11})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{11}q+\frac{1}{2}p-\frac{1}{2}.\frac{8}{11}& \text{Uitwerken } \\ & =pq-\frac{8}{11}q+\frac{1}{2}p-\frac{8}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{8}{11}q+\frac{1}{2}p-\frac{4}{11} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p+\frac{6}{5})(\frac{14}{16}+p)& =(\color{red}{p}+\color{orange}{\frac{6}{5}}).(\color{green}{p}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{8}p+\frac{6}{5}p+\frac{6}{5}.\frac{7}{8}& \text{Uitwerken } \\ & =p^2+(\frac{7}{8}+\frac{6}{5})p+\frac{42}{40} & \text{Neem samen} \\ &=p^2+\frac{83}{40}p+\frac{42}{40} & \text{Maak de som} \\ &=p^2+\frac{83}{40}p+\frac{21}{20} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(\frac{-1}{15}-x)(a-\frac{19}{15})& =(\color{red}{-x}+\color{orange}{\frac{-1}{15}}).(\color{green}{a}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{15}x-\frac{1}{15}a+\frac{1}{15}.\frac{19}{15}& \text{Uitwerken } \\ & =-ax+\frac{19}{15}x-\frac{1}{15}a+\frac{19}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-17}{2})(\frac{-1}{9}-x)& =(\color{red}{x}+\color{orange}{\frac{-17}{2}}).(\color{green}{-x}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-17}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{2})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{1}{9}x+\frac{17}{2}x+\frac{17}{2}.\frac{1}{9}& \text{Uitwerken } \\ & =-x^2+((\frac{-1}{9})+\frac{17}{2})x+(\frac{-17}{18}) & \text{Neem samen} \\ &=-x^2+\frac{151}{18}x+(\frac{-17}{18}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{14}{9}+q)(\frac{19}{3}-a)& =(\color{red}{q}+\color{orange}{\frac{14}{9}}).(\color{green}{-a}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{14}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{19}{3}q-\frac{14}{9}a+\frac{14}{9}.\frac{19}{3}& \text{Uitwerken } \\ & =-aq+\frac{19}{3}q-\frac{14}{9}a+\frac{266}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-7}{6}-a)(\frac{-16}{5}+p)& =(\color{red}{-a}+\color{orange}{\frac{-7}{6}}).(\color{green}{p}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{16}{5}a-\frac{7}{6}p+\frac{7}{6}.\frac{16}{5}& \text{Uitwerken } \\ & =-ap+\frac{16}{5}a-\frac{7}{6}p+\frac{112}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{16}{5}a-\frac{7}{6}p+\frac{56}{15} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-5}{10}-b)(\frac{-15}{6}-x)& =(\color{red}{-b}+\color{orange}{\frac{-1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{2}b+\frac{1}{2}x+\frac{1}{2}.\frac{5}{2}& \text{Uitwerken } \\ & =bx+\frac{5}{2}b+\frac{1}{2}x+\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{15}{14}-a)(\frac{-12}{15}+x)& =(\color{red}{-a}+\color{orange}{\frac{15}{14}}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{15}{14})} . \color{green}{(x)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{5}a+\frac{15}{14}x-\frac{15}{14}.\frac{4}{5}& \text{Uitwerken } \\ & =-ax+\frac{4}{5}a+\frac{15}{14}x-\frac{60}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{4}{5}a+\frac{15}{14}x-\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{8}{6}+x)(\frac{5}{14}-a)& =(\color{red}{x}+\color{orange}{\frac{4}{3}}).(\color{green}{-a}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{14}x-\frac{4}{3}a+\frac{4}{3}.\frac{5}{14}& \text{Uitwerken } \\ & =-ax+\frac{5}{14}x-\frac{4}{3}a+\frac{20}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{5}{14}x-\frac{4}{3}a+\frac{10}{21} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{15}{7}-q)(\frac{16}{3}-p)& =(\color{red}{-q}+\color{orange}{\frac{15}{7}}).(\color{green}{-p}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{15}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{16}{3}q-\frac{15}{7}p+\frac{15}{7}.\frac{16}{3}& \text{Uitwerken } \\ & =pq-\frac{16}{3}q-\frac{15}{7}p+\frac{240}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{16}{3}q-\frac{15}{7}p+\frac{80}{7} & \text{Vereenvoudig} \\\end{align}\)