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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{15}+q)((-13)-x)& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{-x}+\color{blue}{(-13)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(-13)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = -qx-13q+\frac{2}{3}x+\frac{2}{3}.13& \text{Uitwerken } \\ & =-qx-13q+\frac{2}{3}x+\frac{26}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{8}{14})(\frac{-14}{2}+q)& =(\color{red}{a}+\color{orange}{\frac{4}{7}}).(\color{green}{q}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-7)} + \color{orange}{(\frac{4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = aq-7a+\frac{4}{7}q-\frac{4}{7}.7& \text{Uitwerken } \\ & =aq-7a+\frac{4}{7}q-\frac{28}{7} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-7a+\frac{4}{7}q-4 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-7}{7}-x)(b-\frac{3}{2})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{2}x-1b+1.\frac{3}{2}& \text{Uitwerken } \\ & =-bx+\frac{3}{2}x-1b+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-\frac{11}{18})(a-\frac{12}{11})& =(\color{red}{b}+\color{orange}{\frac{-11}{18}}).(\color{green}{a}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{12}{11}b-\frac{11}{18}a+\frac{11}{18}.\frac{12}{11}& \text{Uitwerken } \\ & =ab-\frac{12}{11}b-\frac{11}{18}a+\frac{132}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{12}{11}b-\frac{11}{18}a+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-1}{6}+a)(\frac{-17}{6}+q)& =(\color{red}{a}+\color{orange}{\frac{-1}{6}}).(\color{green}{q}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{6}a-\frac{1}{6}q+\frac{1}{6}.\frac{17}{6}& \text{Uitwerken } \\ & =aq-\frac{17}{6}a-\frac{1}{6}q+\frac{17}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-19}{3}+x)(\frac{1}{10}-q)& =(\color{red}{x}+\color{orange}{\frac{-19}{3}}).(\color{green}{-q}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{10}x+\frac{19}{3}q-\frac{19}{3}.\frac{1}{10}& \text{Uitwerken } \\ & =-qx+\frac{1}{10}x+\frac{19}{3}q-\frac{19}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q-17)(a+(-3))& =(\color{red}{q}+\color{orange}{(-17)}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(-17)} . \color{green}{(a)} + \color{orange}{(-17)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = aq-3q-17a+17.3& \text{Uitwerken } \\ & =aq-3q-17a+51 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-2}{7}-x)(x+\frac{-16}{8})& =(\color{red}{-x}+\color{orange}{\frac{-2}{7}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -xx+2x-\frac{2}{7}x+\frac{2}{7}.2& \text{Uitwerken } \\ & =-x^2+(2+(\frac{-2}{7}))x+(\frac{-4}{7}) & \text{Neem samen} \\ &=-x^2+\frac{12}{7}x+(\frac{-4}{7}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(x+\frac{-9}{10})(p+\frac{-5}{13})& =(\color{red}{x}+\color{orange}{\frac{-9}{10}}).(\color{green}{p}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{13}x-\frac{9}{10}p+\frac{9}{10}.\frac{5}{13}& \text{Uitwerken } \\ & =px-\frac{5}{13}x-\frac{9}{10}p+\frac{45}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{5}{13}x-\frac{9}{10}p+\frac{9}{26} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(x-\frac{-6}{2})(\frac{-11}{9}+q)& =(\color{red}{x}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{9}x+3q-3.\frac{11}{9}& \text{Uitwerken } \\ & =qx-\frac{11}{9}x+3q-\frac{33}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{11}{9}x+3q-\frac{11}{3} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q-\frac{-19}{14})(\frac{-16}{8}-a)& =(\color{red}{q}+\color{orange}{\frac{19}{14}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{19}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -aq-2q-\frac{19}{14}a-\frac{19}{14}.2& \text{Uitwerken } \\ & =-aq-2q-\frac{19}{14}a-\frac{38}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-2q-\frac{19}{14}a-\frac{19}{7} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(b+\frac{-19}{19})(a+\frac{-14}{11})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{14}{11}b-1a+1.\frac{14}{11}& \text{Uitwerken } \\ & =ab-\frac{14}{11}b-1a+\frac{14}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)