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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-9}{19}-q)(a-\frac{-5}{16})& =(\color{red}{-q}+\color{orange}{\frac{-9}{19}}).(\color{green}{a}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{16}q-\frac{9}{19}a-\frac{9}{19}.\frac{5}{16}& \text{Uitwerken } \\ & =-aq-\frac{5}{16}q-\frac{9}{19}a-\frac{45}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{19}{20})(16+x)& =(\color{red}{q}+\color{orange}{\frac{-19}{20}}).(\color{green}{x}+\color{blue}{16})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(16)} + \color{orange}{(\frac{-19}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = qx+16q-\frac{19}{20}x-\frac{19}{20}.16& \text{Uitwerken } \\ & =qx+16q-\frac{19}{20}x-\frac{304}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+16q-\frac{19}{20}x-\frac{76}{5} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{3}{7}-a)(x+\frac{-2}{6})& =(\color{red}{-a}+\color{orange}{\frac{3}{7}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{3}a+\frac{3}{7}x-\frac{3}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =-ax+\frac{1}{3}a+\frac{3}{7}x-\frac{3}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{1}{3}a+\frac{3}{7}x-\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(x-\frac{-5}{11})(\frac{-5}{12}-x)& =(\color{red}{x}+\color{orange}{\frac{5}{11}}).(\color{green}{-x}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{5}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{5}{12}x-\frac{5}{11}x-\frac{5}{11}.\frac{5}{12}& \text{Uitwerken } \\ & =-x^2+((\frac{-5}{12})+(\frac{-5}{11}))x-\frac{25}{132} & \text{Neem samen} \\ &=-x^2-\frac{115}{132}x-\frac{25}{132} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(b+\frac{19}{17})(\frac{-12}{15}+p)& =(\color{red}{b}+\color{orange}{\frac{19}{17}}).(\color{green}{p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{19}{17})} . \color{green}{(p)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{5}b+\frac{19}{17}p-\frac{19}{17}.\frac{4}{5}& \text{Uitwerken } \\ & =bp-\frac{4}{5}b+\frac{19}{17}p-\frac{76}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p+\frac{-15}{16})(q-\frac{-12}{15})& =(\color{red}{p}+\color{orange}{\frac{-15}{16}}).(\color{green}{q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{5}p-\frac{15}{16}q-\frac{15}{16}.\frac{4}{5}& \text{Uitwerken } \\ & =pq+\frac{4}{5}p-\frac{15}{16}q-\frac{60}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{4}{5}p-\frac{15}{16}q-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q+\frac{-20}{13})(\frac{4}{16}+p)& =(\color{red}{q}+\color{orange}{\frac{-20}{13}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{4}q-\frac{20}{13}p-\frac{20}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =pq+\frac{1}{4}q-\frac{20}{13}p-\frac{20}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{4}q-\frac{20}{13}p-\frac{5}{13} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(a-(-10))(\frac{-20}{17}+x)& =(\color{red}{a}+\color{orange}{10}).(\color{green}{x}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(10)} . \color{green}{(x)} + \color{orange}{(10)} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{20}{17}a+10x-10.\frac{20}{17}& \text{Uitwerken } \\ & =ax-\frac{20}{17}a+10x-\frac{200}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{15}{11})(\frac{2}{3}+b)& =(\color{red}{a}+\color{orange}{\frac{-15}{11}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{3}a-\frac{15}{11}b-\frac{15}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =ab+\frac{2}{3}a-\frac{15}{11}b-\frac{30}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{2}{3}a-\frac{15}{11}b-\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(x+\frac{-19}{19})(p-\frac{-9}{4})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{4}x-1p-1.\frac{9}{4}& \text{Uitwerken } \\ & =px+\frac{9}{4}x-1p-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-\frac{-8}{6})(x-\frac{-7}{10})& =(\color{red}{x}+\color{orange}{\frac{4}{3}}).(\color{green}{x}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{7}{10}x+\frac{4}{3}x+\frac{4}{3}.\frac{7}{10}& \text{Uitwerken } \\ & =x^2+(\frac{7}{10}+\frac{4}{3})x+\frac{28}{30} & \text{Neem samen} \\ &=x^2+\frac{61}{30}x+\frac{28}{30} & \text{Maak de som} \\ &=x^2+\frac{61}{30}x+\frac{14}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(\frac{-8}{18}-q)(x-\frac{2}{13})& =(\color{red}{-q}+\color{orange}{\frac{-4}{9}}).(\color{green}{x}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{2}{13}q-\frac{4}{9}x+\frac{4}{9}.\frac{2}{13}& \text{Uitwerken } \\ & =-qx+\frac{2}{13}q-\frac{4}{9}x+\frac{8}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)