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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-19}{13}-p)(\frac{4}{16}-q)& =(\color{red}{-p}+\color{orange}{\frac{-19}{13}}).(\color{green}{-q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{4}p+\frac{19}{13}q-\frac{19}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =pq-\frac{1}{4}p+\frac{19}{13}q-\frac{19}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{-5}{14})(\frac{-14}{4}+q)& =(\color{red}{a}+\color{orange}{\frac{-5}{14}}).(\color{green}{q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{2}a-\frac{5}{14}q+\frac{5}{14}.\frac{7}{2}& \text{Uitwerken } \\ & =aq-\frac{7}{2}a-\frac{5}{14}q+\frac{35}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{7}{2}a-\frac{5}{14}q+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-16}{11}+q)(q+\frac{20}{18})& =(\color{red}{q}+\color{orange}{\frac{-16}{11}}).(\color{green}{q}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{10}{9}q-\frac{16}{11}q-\frac{16}{11}.\frac{10}{9}& \text{Uitwerken } \\ & =q^2+(\frac{10}{9}+(\frac{-16}{11}))q-(\frac{-160}{99}) & \text{Neem samen} \\ &=q^2-\frac{34}{99}q-(\frac{-160}{99}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{-19}{20}-b)(\frac{-10}{18}-b)& =(\color{red}{-b}+\color{orange}{\frac{-19}{20}}).(\color{green}{-b}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{9}b+\frac{19}{20}b+\frac{19}{20}.\frac{5}{9}& \text{Uitwerken } \\ & =b^2+(\frac{5}{9}+\frac{19}{20})b+\frac{95}{180} & \text{Neem samen} \\ &=b^2+\frac{271}{180}b+\frac{95}{180} & \text{Maak de som} \\ &=b^2+\frac{271}{180}b+\frac{19}{36} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(a-\frac{-17}{16})(b+\frac{-4}{12})& =(\color{red}{a}+\color{orange}{\frac{17}{16}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{17}{16})} . \color{green}{(b)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{3}a+\frac{17}{16}b-\frac{17}{16}.\frac{1}{3}& \text{Uitwerken } \\ & =ab-\frac{1}{3}a+\frac{17}{16}b-\frac{17}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-10}{16})(p-\frac{-10}{13})& =(\color{red}{x}+\color{orange}{\frac{-5}{8}}).(\color{green}{p}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{10}{13}x-\frac{5}{8}p-\frac{5}{8}.\frac{10}{13}& \text{Uitwerken } \\ & =px+\frac{10}{13}x-\frac{5}{8}p-\frac{50}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{10}{13}x-\frac{5}{8}p-\frac{25}{52} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(a+\frac{-18}{3})(\frac{-2}{5}-b)& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{-b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(-6)} . \color{green}{(-b)} + \color{orange}{(-6)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{5}a+6b+6.\frac{2}{5}& \text{Uitwerken } \\ & =-ab-\frac{2}{5}a+6b+\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-1}{7}-x)(b-\frac{-13}{8})& =(\color{red}{-x}+\color{orange}{\frac{-1}{7}}).(\color{green}{b}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{8}x-\frac{1}{7}b-\frac{1}{7}.\frac{13}{8}& \text{Uitwerken } \\ & =-bx-\frac{13}{8}x-\frac{1}{7}b-\frac{13}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-11}{8}-p)(b-\frac{16}{4})& =(\color{red}{-p}+\color{orange}{\frac{-11}{8}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(-4)} + \color{orange}{(\frac{-11}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -bp+4p-\frac{11}{8}b+\frac{11}{8}.4& \text{Uitwerken } \\ & =-bp+4p-\frac{11}{8}b+\frac{44}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+4p-\frac{11}{8}b+\frac{11}{2} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-3}{3}+a)(b-\frac{18}{13})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{18}{13}a-1b+1.\frac{18}{13}& \text{Uitwerken } \\ & =ab-\frac{18}{13}a-1b+\frac{18}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{-14}{5})(p+\frac{12}{6})& =(\color{red}{x}+\color{orange}{\frac{-14}{5}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-14}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = px+2x-\frac{14}{5}p-\frac{14}{5}.2& \text{Uitwerken } \\ & =px+2x-\frac{14}{5}p-\frac{28}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{-5}{8})(\frac{-5}{5}-q)& =(\color{red}{q}+\color{orange}{\frac{-5}{8}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-5}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qq-1q+\frac{5}{8}q+\frac{5}{8}.1& \text{Uitwerken } \\ & =-q^2+((-1)+\frac{5}{8})q+(\frac{-5}{8}) & \text{Neem samen} \\ &=-q^2-\frac{3}{8}q+(\frac{-5}{8}) & \text{Maak de som} \\\end{align}\)