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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{16}{20})(\frac{6}{13}-x)& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{-x}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{6}{13}q+\frac{4}{5}x-\frac{4}{5}.\frac{6}{13}& \text{Uitwerken } \\ & =-qx+\frac{6}{13}q+\frac{4}{5}x-\frac{24}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-18}{18}+a)(q+\frac{5}{16})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{16}a-1q-1.\frac{5}{16}& \text{Uitwerken } \\ & =aq+\frac{5}{16}a-1q-\frac{5}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-2}{18}-b)(\frac{-5}{2}+b)& =(\color{red}{-b}+\color{orange}{\frac{-1}{9}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{5}{2}b-\frac{1}{9}b+\frac{1}{9}.\frac{5}{2}& \text{Uitwerken } \\ & =-b^2+(\frac{5}{2}+(\frac{-1}{9}))b+(\frac{-5}{18}) & \text{Neem samen} \\ &=-b^2+\frac{43}{18}b+(\frac{-5}{18}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}((-2)-b)(q+5)& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(5)} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -bq-5b-2q-2.5& \text{Uitwerken } \\ & =-bq-5b-2q-10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{8}{8}+q)(q-\frac{8}{7})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{8}{7}q+1q-1.\frac{8}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-8}{7})+1)q-(\frac{-8}{7}) & \text{Neem samen} \\ &=q^2-\frac{1}{7}q-(\frac{-8}{7}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(x-\frac{-20}{5})(\frac{-14}{11}+b)& =(\color{red}{x}+\color{orange}{4}).(\color{green}{b}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(4)} . \color{green}{(b)} + \color{orange}{(4)} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{14}{11}x+4b-4.\frac{14}{11}& \text{Uitwerken } \\ & =bx-\frac{14}{11}x+4b-\frac{56}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-14}{11}-x)(\frac{-17}{13}+x)& =(\color{red}{-x}+\color{orange}{\frac{-14}{11}}).(\color{green}{x}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{17}{13}x-\frac{14}{11}x+\frac{14}{11}.\frac{17}{13}& \text{Uitwerken } \\ & =-x^2+(\frac{17}{13}+(\frac{-14}{11}))x+(\frac{-238}{143}) & \text{Neem samen} \\ &=-x^2+\frac{5}{143}x+(\frac{-238}{143}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{-19}{20}-a)(p+\frac{-19}{10})& =(\color{red}{-a}+\color{orange}{\frac{-19}{20}}).(\color{green}{p}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{10}a-\frac{19}{20}p+\frac{19}{20}.\frac{19}{10}& \text{Uitwerken } \\ & =-ap+\frac{19}{10}a-\frac{19}{20}p+\frac{361}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q-\frac{-18}{9})(b+\frac{-4}{12})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{3}q+2b-2.\frac{1}{3}& \text{Uitwerken } \\ & =bq-\frac{1}{3}q+2b-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-17}{3}+p)(\frac{5}{16}+x)& =(\color{red}{p}+\color{orange}{\frac{-17}{3}}).(\color{green}{x}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{16}p-\frac{17}{3}x-\frac{17}{3}.\frac{5}{16}& \text{Uitwerken } \\ & =px+\frac{5}{16}p-\frac{17}{3}x-\frac{85}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{4}{10}+b)(a+\frac{-13}{9})& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{9}b+\frac{2}{5}a-\frac{2}{5}.\frac{13}{9}& \text{Uitwerken } \\ & =ab-\frac{13}{9}b+\frac{2}{5}a-\frac{26}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-6}{10}+q)(\frac{6}{12}-p)& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{-p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{2}q+\frac{3}{5}p-\frac{3}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-pq+\frac{1}{2}q+\frac{3}{5}p-\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)