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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{13}{7})(q+\frac{-6}{4})& =(\color{red}{b}+\color{orange}{\frac{13}{7}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{13}{7})} . \color{green}{(q)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{2}b+\frac{13}{7}q-\frac{13}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =bq-\frac{3}{2}b+\frac{13}{7}q-\frac{39}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-8}{12}+q)(\frac{-20}{9}+b)& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{20}{9}q-\frac{2}{3}b+\frac{2}{3}.\frac{20}{9}& \text{Uitwerken } \\ & =bq-\frac{20}{9}q-\frac{2}{3}b+\frac{40}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-8}{6}-p)(p-\frac{-1}{10})& =(\color{red}{-p}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{10}p-\frac{4}{3}p-\frac{4}{3}.\frac{1}{10}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{10})+(\frac{-4}{3}))p-\frac{4}{30} & \text{Neem samen} \\ &=-p^2-\frac{43}{30}p-\frac{4}{30} & \text{Maak de som} \\ &=-p^2-\frac{43}{30}p-\frac{2}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(p+\frac{-2}{14})(\frac{-3}{3}-q)& =(\color{red}{p}+\color{orange}{\frac{-1}{7}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pq-1p+\frac{1}{7}q+\frac{1}{7}.1& \text{Uitwerken } \\ & =-pq-1p+\frac{1}{7}q+\frac{1}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{13}{5}-a)(p-\frac{-2}{11})& =(\color{red}{-a}+\color{orange}{\frac{13}{5}}).(\color{green}{p}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{13}{5})} . \color{green}{(p)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{2}{11}a+\frac{13}{5}p+\frac{13}{5}.\frac{2}{11}& \text{Uitwerken } \\ & =-ap-\frac{2}{11}a+\frac{13}{5}p+\frac{26}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{-20}{15})(b+\frac{5}{12})& =(\color{red}{a}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{12}a-\frac{4}{3}b-\frac{4}{3}.\frac{5}{12}& \text{Uitwerken } \\ & =ab+\frac{5}{12}a-\frac{4}{3}b-\frac{20}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{5}{12}a-\frac{4}{3}b-\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}((-20)+q)(\frac{4}{19}+p)& =(\color{red}{q}+\color{orange}{(-20)}).(\color{green}{p}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(-20)} . \color{green}{(p)} + \color{orange}{(-20)} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{19}q-20p-20.\frac{4}{19}& \text{Uitwerken } \\ & =pq+\frac{4}{19}q-20p-\frac{80}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{10}{11})(\frac{-13}{7}-p)& =(\color{red}{q}+\color{orange}{\frac{-10}{11}}).(\color{green}{-p}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{13}{7}q+\frac{10}{11}p+\frac{10}{11}.\frac{13}{7}& \text{Uitwerken } \\ & =-pq-\frac{13}{7}q+\frac{10}{11}p+\frac{130}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{7}{5}-q)(x-\frac{6}{8})& =(\color{red}{-q}+\color{orange}{\frac{7}{5}}).(\color{green}{x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{4}q+\frac{7}{5}x-\frac{7}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =-qx+\frac{3}{4}q+\frac{7}{5}x-\frac{21}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{16}{7}+a)(b-\frac{4}{17})& =(\color{red}{a}+\color{orange}{\frac{16}{7}}).(\color{green}{b}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{16}{7})} . \color{green}{(b)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{17}a+\frac{16}{7}b-\frac{16}{7}.\frac{4}{17}& \text{Uitwerken } \\ & =ab-\frac{4}{17}a+\frac{16}{7}b-\frac{64}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-4}{5}+b)(b+\frac{-20}{14})& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{b}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{10}{7}b-\frac{4}{5}b+\frac{4}{5}.\frac{10}{7}& \text{Uitwerken } \\ & =b^2+((\frac{-10}{7})+(\frac{-4}{5}))b+\frac{40}{35} & \text{Neem samen} \\ &=b^2-\frac{78}{35}b+\frac{40}{35} & \text{Maak de som} \\ &=b^2-\frac{78}{35}b+\frac{8}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(\frac{8}{10}+q)(\frac{19}{12}-a)& =(\color{red}{q}+\color{orange}{\frac{4}{5}}).(\color{green}{-a}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{19}{12}q-\frac{4}{5}a+\frac{4}{5}.\frac{19}{12}& \text{Uitwerken } \\ & =-aq+\frac{19}{12}q-\frac{4}{5}a+\frac{76}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{19}{12}q-\frac{4}{5}a+\frac{19}{15} & \text{Vereenvoudig} \\\end{align}\)