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

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Werk uit en vereenvoudig

1. \((q+\frac{20}{6})(x-\frac{-16}{19})\)
2. \((\frac{-14}{4}+a)(\frac{1}{5}+q)\)
3. \((q-\frac{-17}{6})(\frac{-18}{9}+p)\)
4. \((a-\frac{7}{17})(x+(-13))\)
5. \((a-\frac{6}{15})(x+\frac{-10}{13})\)
6. \((a-\frac{-2}{16})(q-\frac{-4}{20})\)
7. \((b+\frac{13}{6})(x-\frac{-3}{10})\)
8. \((p+\frac{-5}{19})(\frac{16}{4}+q)\)
9. \((\frac{4}{12}-a)(q-\frac{-8}{4})\)
10. \((\frac{-5}{9}-p)(x-\frac{-4}{10})\)
11. \((\frac{8}{6}-b)(\frac{-7}{17}-q)\)
12. \((\frac{-19}{5}+q)(q+\frac{-7}{12})\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{20}{6})(x-\frac{-16}{19})& =(\color{red}{q}+\color{orange}{\frac{10}{3}}).(\color{green}{x}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{16}{19}q+\frac{10}{3}x+\frac{10}{3}.\frac{16}{19}& \text{Uitwerken } \\ & =qx+\frac{16}{19}q+\frac{10}{3}x+\frac{160}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-14}{4}+a)(\frac{1}{5}+q)& =(\color{red}{a}+\color{orange}{\frac{-7}{2}}).(\color{green}{q}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{5}a-\frac{7}{2}q-\frac{7}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =aq+\frac{1}{5}a-\frac{7}{2}q-\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{-17}{6})(\frac{-18}{9}+p)& =(\color{red}{q}+\color{orange}{\frac{17}{6}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{17}{6})} . \color{green}{(p)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2q+\frac{17}{6}p-\frac{17}{6}.2& \text{Uitwerken } \\ & =pq-2q+\frac{17}{6}p-\frac{34}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-2q+\frac{17}{6}p-\frac{17}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(a-\frac{7}{17})(x+(-13))& =(\color{red}{a}+\color{orange}{\frac{-7}{17}}).(\color{green}{x}+\color{blue}{(-13)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-13)} + \color{orange}{(\frac{-7}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = ax-13a-\frac{7}{17}x+\frac{7}{17}.13& \text{Uitwerken } \\ & =ax-13a-\frac{7}{17}x+\frac{91}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{6}{15})(x+\frac{-10}{13})& =(\color{red}{a}+\color{orange}{\frac{-2}{5}}).(\color{green}{x}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{10}{13}a-\frac{2}{5}x+\frac{2}{5}.\frac{10}{13}& \text{Uitwerken } \\ & =ax-\frac{10}{13}a-\frac{2}{5}x+\frac{20}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{10}{13}a-\frac{2}{5}x+\frac{4}{13} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(a-\frac{-2}{16})(q-\frac{-4}{20})& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{q}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{1}{8})} . \color{green}{(q)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{5}a+\frac{1}{8}q+\frac{1}{8}.\frac{1}{5}& \text{Uitwerken } \\ & =aq+\frac{1}{5}a+\frac{1}{8}q+\frac{1}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{13}{6})(x-\frac{-3}{10})& =(\color{red}{b}+\color{orange}{\frac{13}{6}}).(\color{green}{x}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{13}{6})} . \color{green}{(x)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{10}b+\frac{13}{6}x+\frac{13}{6}.\frac{3}{10}& \text{Uitwerken } \\ & =bx+\frac{3}{10}b+\frac{13}{6}x+\frac{39}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{10}b+\frac{13}{6}x+\frac{13}{20} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(p+\frac{-5}{19})(\frac{16}{4}+q)& =(\color{red}{p}+\color{orange}{\frac{-5}{19}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{-5}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = pq+4p-\frac{5}{19}q-\frac{5}{19}.4& \text{Uitwerken } \\ & =pq+4p-\frac{5}{19}q-\frac{20}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{4}{12}-a)(q-\frac{-8}{4})& =(\color{red}{-a}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -aq-2a+\frac{1}{3}q+\frac{1}{3}.2& \text{Uitwerken } \\ & =-aq-2a+\frac{1}{3}q+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-5}{9}-p)(x-\frac{-4}{10})& =(\color{red}{-p}+\color{orange}{\frac{-5}{9}}).(\color{green}{x}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{5}p-\frac{5}{9}x-\frac{5}{9}.\frac{2}{5}& \text{Uitwerken } \\ & =-px-\frac{2}{5}p-\frac{5}{9}x-\frac{10}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{2}{5}p-\frac{5}{9}x-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{8}{6}-b)(\frac{-7}{17}-q)& =(\color{red}{-b}+\color{orange}{\frac{4}{3}}).(\color{green}{-q}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{17}b-\frac{4}{3}q-\frac{4}{3}.\frac{7}{17}& \text{Uitwerken } \\ & =bq+\frac{7}{17}b-\frac{4}{3}q-\frac{28}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-19}{5}+q)(q+\frac{-7}{12})& =(\color{red}{q}+\color{orange}{\frac{-19}{5}}).(\color{green}{q}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{12}q-\frac{19}{5}q+\frac{19}{5}.\frac{7}{12}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{12})+(\frac{-19}{5}))q+\frac{133}{60} & \text{Neem samen} \\ &=q^2-\frac{263}{60}q+\frac{133}{60} & \text{Maak de som} \\\end{align}\)