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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-20}{19}-a)(\frac{-15}{8}-p)& =(\color{red}{-a}+\color{orange}{\frac{-20}{19}}).(\color{green}{-p}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{-20}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{15}{8}a+\frac{20}{19}p+\frac{20}{19}.\frac{15}{8}& \text{Uitwerken } \\ & =ap+\frac{15}{8}a+\frac{20}{19}p+\frac{300}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{15}{8}a+\frac{20}{19}p+\frac{75}{38} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(q-\frac{6}{7})(a+\frac{-13}{20})& =(\color{red}{q}+\color{orange}{\frac{-6}{7}}).(\color{green}{a}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{20}q-\frac{6}{7}a+\frac{6}{7}.\frac{13}{20}& \text{Uitwerken } \\ & =aq-\frac{13}{20}q-\frac{6}{7}a+\frac{78}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{13}{20}q-\frac{6}{7}a+\frac{39}{70} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b+\frac{5}{15})(q-\frac{-19}{10})& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{10}b+\frac{1}{3}q+\frac{1}{3}.\frac{19}{10}& \text{Uitwerken } \\ & =bq+\frac{19}{10}b+\frac{1}{3}q+\frac{19}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{1}{11}-a)(\frac{9}{15}-x)& =(\color{red}{-a}+\color{orange}{\frac{1}{11}}).(\color{green}{-x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{1}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{5}a-\frac{1}{11}x+\frac{1}{11}.\frac{3}{5}& \text{Uitwerken } \\ & =ax-\frac{3}{5}a-\frac{1}{11}x+\frac{3}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{-4}{8})(\frac{-5}{13}-q)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{-q}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{13}b-\frac{1}{2}q-\frac{1}{2}.\frac{5}{13}& \text{Uitwerken } \\ & =-bq-\frac{5}{13}b-\frac{1}{2}q-\frac{5}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{-17}{10})(\frac{-20}{7}+p)& =(\color{red}{q}+\color{orange}{\frac{-17}{10}}).(\color{green}{p}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{20}{7}q-\frac{17}{10}p+\frac{17}{10}.\frac{20}{7}& \text{Uitwerken } \\ & =pq-\frac{20}{7}q-\frac{17}{10}p+\frac{340}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{20}{7}q-\frac{17}{10}p+\frac{34}{7} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-17}{2}+x)(\frac{-9}{5}-x)& =(\color{red}{x}+\color{orange}{\frac{-17}{2}}).(\color{green}{-x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-17}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{2})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{9}{5}x+\frac{17}{2}x+\frac{17}{2}.\frac{9}{5}& \text{Uitwerken } \\ & =-x^2+((\frac{-9}{5})+\frac{17}{2})x+(\frac{-153}{10}) & \text{Neem samen} \\ &=-x^2+\frac{67}{10}x+(\frac{-153}{10}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{8}{14}+p)(\frac{-4}{12}-q)& =(\color{red}{p}+\color{orange}{\frac{4}{7}}).(\color{green}{-q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{4}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{3}p-\frac{4}{7}q-\frac{4}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =-pq-\frac{1}{3}p-\frac{4}{7}q-\frac{4}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{17}{9}-b)(b-\frac{-14}{10})& =(\color{red}{-b}+\color{orange}{\frac{17}{9}}).(\color{green}{b}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{17}{9})} . \color{green}{(b)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{5}b+\frac{17}{9}b+\frac{17}{9}.\frac{7}{5}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{5})+\frac{17}{9})b+(\frac{-119}{45}) & \text{Neem samen} \\ &=-b^2+\frac{22}{45}b+(\frac{-119}{45}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(p-\frac{7}{19})(\frac{14}{18}+b)& =(\color{red}{p}+\color{orange}{\frac{-7}{19}}).(\color{green}{b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-7}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{9}p-\frac{7}{19}b-\frac{7}{19}.\frac{7}{9}& \text{Uitwerken } \\ & =bp+\frac{7}{9}p-\frac{7}{19}b-\frac{49}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{13}{11}-b)(\frac{13}{5}+q)& =(\color{red}{-b}+\color{orange}{\frac{13}{11}}).(\color{green}{q}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{13}{11})} . \color{green}{(q)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{5}b+\frac{13}{11}q+\frac{13}{11}.\frac{13}{5}& \text{Uitwerken } \\ & =-bq-\frac{13}{5}b+\frac{13}{11}q+\frac{169}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{3}{10}-x)(a+\frac{1}{6})& =(\color{red}{-x}+\color{orange}{\frac{3}{10}}).(\color{green}{a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{6}x+\frac{3}{10}a+\frac{3}{10}.\frac{1}{6}& \text{Uitwerken } \\ & =-ax-\frac{1}{6}x+\frac{3}{10}a+\frac{3}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{1}{6}x+\frac{3}{10}a+\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)