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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{20}{14})(x-\frac{12}{3})& =(\color{red}{q}+\color{orange}{\frac{-10}{7}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(\frac{-10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = qx-4q-\frac{10}{7}x+\frac{10}{7}.4& \text{Uitwerken } \\ & =qx-4q-\frac{10}{7}x+\frac{40}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p+\frac{17}{7})(q-\frac{19}{11})& =(\color{red}{p}+\color{orange}{\frac{17}{7}}).(\color{green}{q}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{17}{7})} . \color{green}{(q)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{11}p+\frac{17}{7}q-\frac{17}{7}.\frac{19}{11}& \text{Uitwerken } \\ & =pq-\frac{19}{11}p+\frac{17}{7}q-\frac{323}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-13}{13}+q)(a+\frac{-20}{16})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{4}q-1a+1.\frac{5}{4}& \text{Uitwerken } \\ & =aq-\frac{5}{4}q-1a+\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{14}{7}+q)(\frac{-12}{10}-b)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{-b}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(2)} . \color{green}{(-b)} + \color{orange}{(2)} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{6}{5}q-2b-2.\frac{6}{5}& \text{Uitwerken } \\ & =-bq-\frac{6}{5}q-2b-\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-1}{19}-a)(b+\frac{10}{2})& =(\color{red}{-a}+\color{orange}{\frac{-1}{19}}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(5)} + \color{orange}{(\frac{-1}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -ab-5a-\frac{1}{19}b-\frac{1}{19}.5& \text{Uitwerken } \\ & =-ab-5a-\frac{1}{19}b-\frac{5}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}((-20)+p)(p+\frac{1}{16})& =(\color{red}{p}+\color{orange}{(-20)}).(\color{green}{p}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(-20)} . \color{green}{(p)} + \color{orange}{(-20)} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{16}p-20p-20.\frac{1}{16}& \text{Uitwerken } \\ & =p^2+(\frac{1}{16}+(-20))p-(\frac{-20}{16}) & \text{Neem samen} \\ &=p^2-\frac{319}{16}p-(\frac{-20}{16}) & \text{Maak de som} \\ &=p^2-\frac{319}{16}p+\frac{5}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
7. \(\begin{align}(\frac{-12}{18}-x)(x+\frac{-1}{20})& =(\color{red}{-x}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{20}x-\frac{2}{3}x+\frac{2}{3}.\frac{1}{20}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{20}+(\frac{-2}{3}))x+(\frac{-2}{60}) & \text{Neem samen} \\ &=-x^2-\frac{37}{60}x+(\frac{-2}{60}) & \text{Maak de som} \\ &=-x^2-\frac{37}{60}x+(\frac{-1}{30}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(x-\frac{13}{13})(a+\frac{13}{9})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{13}{9}x-1a-1.\frac{13}{9}& \text{Uitwerken } \\ & =ax+\frac{13}{9}x-1a-\frac{13}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-3}{13}-q)(\frac{-18}{18}-p)& =(\color{red}{-q}+\color{orange}{\frac{-3}{13}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-3}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq+1q+\frac{3}{13}p+\frac{3}{13}.1& \text{Uitwerken } \\ & =pq+1q+\frac{3}{13}p+\frac{3}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a-\frac{-17}{19})(\frac{-18}{4}-p)& =(\color{red}{a}+\color{orange}{\frac{17}{19}}).(\color{green}{-p}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{17}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{2}a-\frac{17}{19}p-\frac{17}{19}.\frac{9}{2}& \text{Uitwerken } \\ & =-ap-\frac{9}{2}a-\frac{17}{19}p-\frac{153}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{-3}{2})(x+\frac{-1}{6})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{6}a+\frac{3}{2}x-\frac{3}{2}.\frac{1}{6}& \text{Uitwerken } \\ & =ax-\frac{1}{6}a+\frac{3}{2}x-\frac{3}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{1}{6}a+\frac{3}{2}x-\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(p-\frac{5}{19})(a-\frac{-3}{6})& =(\color{red}{p}+\color{orange}{\frac{-5}{19}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}p-\frac{5}{19}a-\frac{5}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}p-\frac{5}{19}a-\frac{5}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)