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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}((-12)-q)(q+\frac{18}{6})& =(\color{red}{-q}+\color{orange}{(-12)}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(3)} + \color{orange}{(-12)} . \color{green}{(q)} + \color{orange}{(-12)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -qq-3q-12q-12.3& \text{Uitwerken } \\ & =-q^2+((-3)+(-12))q-36 & \text{Neem samen} \\ &=-q^2-15q-36 & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{-18}{6}-b)(\frac{-15}{10}+p)& =(\color{red}{-b}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{3}{2}b-3p+3.\frac{3}{2}& \text{Uitwerken } \\ & =-bp+\frac{3}{2}b-3p+\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-9}{3}+q)(a-(-13))& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{13})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(13)} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = aq+13q-3a-3.13& \text{Uitwerken } \\ & =aq+13q-3a-39 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{10}{13})(x+\frac{-10}{3})& =(\color{red}{p}+\color{orange}{\frac{10}{13}}).(\color{green}{x}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{10}{13})} . \color{green}{(x)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{3}p+\frac{10}{13}x-\frac{10}{13}.\frac{10}{3}& \text{Uitwerken } \\ & =px-\frac{10}{3}p+\frac{10}{13}x-\frac{100}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p-\frac{-13}{5})(\frac{-10}{9}+p)& =(\color{red}{p}+\color{orange}{\frac{13}{5}}).(\color{green}{p}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{13}{5})} . \color{green}{(p)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{10}{9}p+\frac{13}{5}p-\frac{13}{5}.\frac{10}{9}& \text{Uitwerken } \\ & =p^2+((\frac{-10}{9})+\frac{13}{5})p-(\frac{-130}{45}) & \text{Neem samen} \\ &=p^2+\frac{67}{45}p-(\frac{-130}{45}) & \text{Maak de som} \\ &=p^2+\frac{67}{45}p+\frac{26}{9} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
6. \(\begin{align}(\frac{-19}{18}+p)(\frac{-19}{10}-p)& =(\color{red}{p}+\color{orange}{\frac{-19}{18}}).(\color{green}{-p}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{19}{10}p+\frac{19}{18}p+\frac{19}{18}.\frac{19}{10}& \text{Uitwerken } \\ & =-p^2+((\frac{-19}{10})+\frac{19}{18})p+(\frac{-361}{180}) & \text{Neem samen} \\ &=-p^2-\frac{76}{90}p+(\frac{-361}{180}) & \text{Maak de som} \\ &=-p^2-\frac{38}{45}p+(\frac{-361}{180}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(q-\frac{-10}{2})(\frac{7}{4}+q)& =(\color{red}{q}+\color{orange}{5}).(\color{green}{q}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(5)} . \color{green}{(q)} + \color{orange}{(5)} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{4}q+5q+5.\frac{7}{4}& \text{Uitwerken } \\ & =q^2+(\frac{7}{4}+5)q+\frac{35}{4} & \text{Neem samen} \\ &=q^2+\frac{27}{4}q+\frac{35}{4} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{-1}{3}+x)(b-\frac{13}{10})& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{10}x-\frac{1}{3}b+\frac{1}{3}.\frac{13}{10}& \text{Uitwerken } \\ & =bx-\frac{13}{10}x-\frac{1}{3}b+\frac{13}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{6}{19}-q)(\frac{-8}{7}+b)& =(\color{red}{-q}+\color{orange}{\frac{6}{19}}).(\color{green}{b}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{6}{19})} . \color{green}{(b)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{8}{7}q+\frac{6}{19}b-\frac{6}{19}.\frac{8}{7}& \text{Uitwerken } \\ & =-bq+\frac{8}{7}q+\frac{6}{19}b-\frac{48}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{13}{17}+x)(x+\frac{4}{2})& =(\color{red}{x}+\color{orange}{\frac{13}{17}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{13}{17})} . \color{green}{(x)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = xx+2x+\frac{13}{17}x+\frac{13}{17}.2& \text{Uitwerken } \\ & =x^2+(2+\frac{13}{17})x+\frac{26}{17} & \text{Neem samen} \\ &=x^2+\frac{47}{17}x+\frac{26}{17} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-16}{10}+a)(\frac{-1}{13}+q)& =(\color{red}{a}+\color{orange}{\frac{-8}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{13}a-\frac{8}{5}q+\frac{8}{5}.\frac{1}{13}& \text{Uitwerken } \\ & =aq-\frac{1}{13}a-\frac{8}{5}q+\frac{8}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(7-a)(\frac{1}{11}-b)& =(\color{red}{-a}+\color{orange}{7}).(\color{green}{-b}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(7)} . \color{green}{(-b)} + \color{orange}{(7)} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{11}a-7b+7.\frac{1}{11}& \text{Uitwerken } \\ & =ab-\frac{1}{11}a-7b+\frac{7}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)