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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{5}{14}+b)(\frac{1}{4}-b)& =(\color{red}{b}+\color{orange}{\frac{5}{14}}).(\color{green}{-b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{5}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{4}b-\frac{5}{14}b+\frac{5}{14}.\frac{1}{4}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{4}+(\frac{-5}{14}))b+(\frac{-5}{56}) & \text{Neem samen} \\ &=-b^2-\frac{3}{28}b+(\frac{-5}{56}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(x-\frac{3}{3})(\frac{3}{14}+b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{14}x-1b-1.\frac{3}{14}& \text{Uitwerken } \\ & =bx+\frac{3}{14}x-1b-\frac{3}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a+\frac{8}{4})(x+\frac{-4}{4})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a+2x-2.1& \text{Uitwerken } \\ & =ax-1a+2x-2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{3}{5}+p)(p+\frac{-3}{15})& =(\color{red}{p}+\color{orange}{\frac{3}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{5}p+\frac{3}{5}p-\frac{3}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{5})+\frac{3}{5})p-(\frac{-3}{25}) & \text{Neem samen} \\ &=p^2+\frac{2}{5}p-(\frac{-3}{25}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(x-\frac{18}{11})(a+\frac{19}{13})& =(\color{red}{x}+\color{orange}{\frac{-18}{11}}).(\color{green}{a}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(\frac{-18}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{13}x-\frac{18}{11}a-\frac{18}{11}.\frac{19}{13}& \text{Uitwerken } \\ & =ax+\frac{19}{13}x-\frac{18}{11}a-\frac{342}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-\frac{-8}{4})(p-\frac{-7}{5})& =(\color{red}{p}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{5}p+2p+2.\frac{7}{5}& \text{Uitwerken } \\ & =p^2+(\frac{7}{5}+2)p+\frac{14}{5} & \text{Neem samen} \\ &=p^2+\frac{17}{5}p+\frac{14}{5} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(b-\frac{2}{10})(a+\frac{13}{12})& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{12}b-\frac{1}{5}a-\frac{1}{5}.\frac{13}{12}& \text{Uitwerken } \\ & =ab+\frac{13}{12}b-\frac{1}{5}a-\frac{13}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a-\frac{-3}{17})(\frac{-1}{14}-x)& =(\color{red}{a}+\color{orange}{\frac{3}{17}}).(\color{green}{-x}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{3}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{14}a-\frac{3}{17}x-\frac{3}{17}.\frac{1}{14}& \text{Uitwerken } \\ & =-ax-\frac{1}{14}a-\frac{3}{17}x-\frac{3}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-10}{9}-q)(a-\frac{7}{3})& =(\color{red}{-q}+\color{orange}{\frac{-10}{9}}).(\color{green}{a}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{3}q-\frac{10}{9}a+\frac{10}{9}.\frac{7}{3}& \text{Uitwerken } \\ & =-aq+\frac{7}{3}q-\frac{10}{9}a+\frac{70}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b-\frac{6}{10})(a+\frac{17}{16})& =(\color{red}{b}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{16}b-\frac{3}{5}a-\frac{3}{5}.\frac{17}{16}& \text{Uitwerken } \\ & =ab+\frac{17}{16}b-\frac{3}{5}a-\frac{51}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{-12}{15})(a+\frac{4}{11})& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{a}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{11}p-\frac{4}{5}a-\frac{4}{5}.\frac{4}{11}& \text{Uitwerken } \\ & =ap+\frac{4}{11}p-\frac{4}{5}a-\frac{16}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{8}{10})(\frac{-6}{5}-x)& =(\color{red}{q}+\color{orange}{\frac{4}{5}}).(\color{green}{-x}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{6}{5}q-\frac{4}{5}x-\frac{4}{5}.\frac{6}{5}& \text{Uitwerken } \\ & =-qx-\frac{6}{5}q-\frac{4}{5}x-\frac{24}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)