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

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1. \((q-\frac{-11}{17})(q-\frac{-4}{2})\)
2. \((a+\frac{5}{4})(\frac{-13}{16}+x)\)
3. \((p+\frac{-11}{16})(\frac{2}{8}-p)\)
4. \((\frac{10}{20}+x)(\frac{17}{5}-b)\)
5. \((\frac{12}{2}-b)(\frac{4}{19}-a)\)
6. \((a+\frac{-11}{15})(\frac{-2}{16}+x)\)
7. \((\frac{19}{14}-a)(\frac{2}{15}+p)\)
8. \((b-\frac{-14}{17})(\frac{-17}{4}+x)\)
9. \((p-\frac{-9}{18})(\frac{1}{17}+x)\)
10. \((\frac{-19}{8}+p)(x-\frac{17}{6})\)
11. \((\frac{17}{10}+b)(\frac{13}{14}-p)\)
12. \((\frac{1}{7}-a)((-5)-x)\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-11}{17})(q-\frac{-4}{2})& =(\color{red}{q}+\color{orange}{\frac{11}{17}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{11}{17})} . \color{green}{(q)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qq+2q+\frac{11}{17}q+\frac{11}{17}.2& \text{Uitwerken } \\ & =q^2+(2+\frac{11}{17})q+\frac{22}{17} & \text{Neem samen} \\ &=q^2+\frac{45}{17}q+\frac{22}{17} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(a+\frac{5}{4})(\frac{-13}{16}+x)& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{x}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{16}a+\frac{5}{4}x-\frac{5}{4}.\frac{13}{16}& \text{Uitwerken } \\ & =ax-\frac{13}{16}a+\frac{5}{4}x-\frac{65}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{-11}{16})(\frac{2}{8}-p)& =(\color{red}{p}+\color{orange}{\frac{-11}{16}}).(\color{green}{-p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{1}{4}p+\frac{11}{16}p-\frac{11}{16}.\frac{1}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{1}{4}+\frac{11}{16})p-\frac{11}{64} & \text{Neem samen} \\ &=-p^2+\frac{15}{16}p-\frac{11}{64} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{10}{20}+x)(\frac{17}{5}-b)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{-b}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{17}{5}x-\frac{1}{2}b+\frac{1}{2}.\frac{17}{5}& \text{Uitwerken } \\ & =-bx+\frac{17}{5}x-\frac{1}{2}b+\frac{17}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{12}{2}-b)(\frac{4}{19}-a)& =(\color{red}{-b}+\color{orange}{6}).(\color{green}{-a}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(6)} . \color{green}{(-a)} + \color{orange}{(6)} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{19}b-6a+6.\frac{4}{19}& \text{Uitwerken } \\ & =ab-\frac{4}{19}b-6a+\frac{24}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{-11}{15})(\frac{-2}{16}+x)& =(\color{red}{a}+\color{orange}{\frac{-11}{15}}).(\color{green}{x}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{8}a-\frac{11}{15}x+\frac{11}{15}.\frac{1}{8}& \text{Uitwerken } \\ & =ax-\frac{1}{8}a-\frac{11}{15}x+\frac{11}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{19}{14}-a)(\frac{2}{15}+p)& =(\color{red}{-a}+\color{orange}{\frac{19}{14}}).(\color{green}{p}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(\frac{19}{14})} . \color{green}{(p)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{2}{15}a+\frac{19}{14}p+\frac{19}{14}.\frac{2}{15}& \text{Uitwerken } \\ & =-ap-\frac{2}{15}a+\frac{19}{14}p+\frac{38}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{2}{15}a+\frac{19}{14}p+\frac{19}{105} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(b-\frac{-14}{17})(\frac{-17}{4}+x)& =(\color{red}{b}+\color{orange}{\frac{14}{17}}).(\color{green}{x}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{14}{17})} . \color{green}{(x)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{4}b+\frac{14}{17}x-\frac{14}{17}.\frac{17}{4}& \text{Uitwerken } \\ & =bx-\frac{17}{4}b+\frac{14}{17}x-\frac{238}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{17}{4}b+\frac{14}{17}x-\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(p-\frac{-9}{18})(\frac{1}{17}+x)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{17}p+\frac{1}{2}x+\frac{1}{2}.\frac{1}{17}& \text{Uitwerken } \\ & =px+\frac{1}{17}p+\frac{1}{2}x+\frac{1}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-19}{8}+p)(x-\frac{17}{6})& =(\color{red}{p}+\color{orange}{\frac{-19}{8}}).(\color{green}{x}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-19}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{6}p-\frac{19}{8}x+\frac{19}{8}.\frac{17}{6}& \text{Uitwerken } \\ & =px-\frac{17}{6}p-\frac{19}{8}x+\frac{323}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{17}{10}+b)(\frac{13}{14}-p)& =(\color{red}{b}+\color{orange}{\frac{17}{10}}).(\color{green}{-p}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{17}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{14}b-\frac{17}{10}p+\frac{17}{10}.\frac{13}{14}& \text{Uitwerken } \\ & =-bp+\frac{13}{14}b-\frac{17}{10}p+\frac{221}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{1}{7}-a)((-5)-x)& =(\color{red}{-a}+\color{orange}{\frac{1}{7}}).(\color{green}{-x}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(-5)} + \color{orange}{(\frac{1}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = ax+5a-\frac{1}{7}x-\frac{1}{7}.5& \text{Uitwerken } \\ & =ax+5a-\frac{1}{7}x-\frac{5}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)