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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-1}{15}-p)(\frac{-15}{10}-b)& =(\color{red}{-p}+\color{orange}{\frac{-1}{15}}).(\color{green}{-b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{2}p+\frac{1}{15}b+\frac{1}{15}.\frac{3}{2}& \text{Uitwerken } \\ & =bp+\frac{3}{2}p+\frac{1}{15}b+\frac{3}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{3}{2}p+\frac{1}{15}b+\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p-\frac{-8}{10})(\frac{5}{6}+p)& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{6}p+\frac{4}{5}p+\frac{4}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =p^2+(\frac{5}{6}+\frac{4}{5})p+\frac{20}{30} & \text{Neem samen} \\ &=p^2+\frac{49}{30}p+\frac{20}{30} & \text{Maak de som} \\ &=p^2+\frac{49}{30}p+\frac{2}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
3. \(\begin{align}(q+13)(q-\frac{15}{6})& =(\color{red}{q}+\color{orange}{13}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(13)} . \color{green}{(q)} + \color{orange}{(13)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{5}{2}q+13q-13.\frac{5}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-5}{2})+13)q-(\frac{-65}{2}) & \text{Neem samen} \\ &=q^2+\frac{21}{2}q-(\frac{-65}{2}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(q-\frac{-12}{18})(a-\frac{12}{14})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{6}{7}q+\frac{2}{3}a-\frac{2}{3}.\frac{6}{7}& \text{Uitwerken } \\ & =aq-\frac{6}{7}q+\frac{2}{3}a-\frac{12}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{6}{7}q+\frac{2}{3}a-\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{5}{10}+p)(p+\frac{-11}{11})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pp-1p+\frac{1}{2}p-\frac{1}{2}.1& \text{Uitwerken } \\ & =p^2+((-1)+\frac{1}{2})p-(\frac{-1}{2}) & \text{Neem samen} \\ &=p^2-\frac{1}{2}p-(\frac{-1}{2}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(p+\frac{-16}{3})(\frac{-19}{13}-q)& =(\color{red}{p}+\color{orange}{\frac{-16}{3}}).(\color{green}{-q}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{-16}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{13}p+\frac{16}{3}q+\frac{16}{3}.\frac{19}{13}& \text{Uitwerken } \\ & =-pq-\frac{19}{13}p+\frac{16}{3}q+\frac{304}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-7}{10}+p)(\frac{14}{19}+b)& =(\color{red}{p}+\color{orange}{\frac{-7}{10}}).(\color{green}{b}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{14}{19}p-\frac{7}{10}b-\frac{7}{10}.\frac{14}{19}& \text{Uitwerken } \\ & =bp+\frac{14}{19}p-\frac{7}{10}b-\frac{98}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{14}{19}p-\frac{7}{10}b-\frac{49}{95} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-16}{7}-q)(\frac{8}{19}-b)& =(\color{red}{-q}+\color{orange}{\frac{-16}{7}}).(\color{green}{-b}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{19}q+\frac{16}{7}b-\frac{16}{7}.\frac{8}{19}& \text{Uitwerken } \\ & =bq-\frac{8}{19}q+\frac{16}{7}b-\frac{128}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p+\frac{-9}{16})(p+\frac{-14}{7})& =(\color{red}{p}+\color{orange}{\frac{-9}{16}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-9}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pp-2p-\frac{9}{16}p+\frac{9}{16}.2& \text{Uitwerken } \\ & =p^2+((-2)+(\frac{-9}{16}))p+\frac{18}{16} & \text{Neem samen} \\ &=p^2-\frac{41}{16}p+\frac{18}{16} & \text{Maak de som} \\ &=p^2-\frac{41}{16}p+\frac{9}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(q-\frac{-10}{8})(\frac{10}{15}-p)& =(\color{red}{q}+\color{orange}{\frac{5}{4}}).(\color{green}{-p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{2}{3}q-\frac{5}{4}p+\frac{5}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =-pq+\frac{2}{3}q-\frac{5}{4}p+\frac{10}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{2}{3}q-\frac{5}{4}p+\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{5}{20}+q)(\frac{15}{10}-p)& =(\color{red}{q}+\color{orange}{\frac{1}{4}}).(\color{green}{-p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{2}q-\frac{1}{4}p+\frac{1}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =-pq+\frac{3}{2}q-\frac{1}{4}p+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{15}{10})(p+\frac{-3}{15})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{5}q-\frac{3}{2}p+\frac{3}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =pq-\frac{1}{5}q-\frac{3}{2}p+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)