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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{20}{7})(p+\frac{17}{8})& =(\color{red}{p}+\color{orange}{\frac{-20}{7}}).(\color{green}{p}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{8}p-\frac{20}{7}p-\frac{20}{7}.\frac{17}{8}& \text{Uitwerken } \\ & =p^2+(\frac{17}{8}+(\frac{-20}{7}))p-(\frac{-340}{56}) & \text{Neem samen} \\ &=p^2-\frac{41}{56}p-(\frac{-340}{56}) & \text{Maak de som} \\ &=p^2-\frac{41}{56}p+\frac{85}{14} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
2. \(\begin{align}(\frac{11}{11}+b)(\frac{-1}{7}+q)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{7}b+1q-1.\frac{1}{7}& \text{Uitwerken } \\ & =bq-\frac{1}{7}b+1q-\frac{1}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+\frac{4}{19})(q+\frac{20}{3})& =(\color{red}{q}+\color{orange}{\frac{4}{19}}).(\color{green}{q}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{4}{19})} . \color{green}{(q)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{20}{3}q+\frac{4}{19}q+\frac{4}{19}.\frac{20}{3}& \text{Uitwerken } \\ & =q^2+(\frac{20}{3}+\frac{4}{19})q+\frac{80}{57} & \text{Neem samen} \\ &=q^2+\frac{392}{57}q+\frac{80}{57} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{-14}{19}+x)(a+\frac{7}{2})& =(\color{red}{x}+\color{orange}{\frac{-14}{19}}).(\color{green}{a}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{2}x-\frac{14}{19}a-\frac{14}{19}.\frac{7}{2}& \text{Uitwerken } \\ & =ax+\frac{7}{2}x-\frac{14}{19}a-\frac{98}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{7}{2}x-\frac{14}{19}a-\frac{49}{19} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-15}{2}+p)(p-\frac{-20}{17})& =(\color{red}{p}+\color{orange}{\frac{-15}{2}}).(\color{green}{p}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{20}{17}p-\frac{15}{2}p-\frac{15}{2}.\frac{20}{17}& \text{Uitwerken } \\ & =p^2+(\frac{20}{17}+(\frac{-15}{2}))p-(\frac{-300}{34}) & \text{Neem samen} \\ &=p^2-\frac{215}{34}p-(\frac{-300}{34}) & \text{Maak de som} \\ &=p^2-\frac{215}{34}p+\frac{150}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
6. \(\begin{align}(\frac{12}{5}-x)(x-\frac{4}{7})& =(\color{red}{-x}+\color{orange}{\frac{12}{5}}).(\color{green}{x}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{12}{5})} . \color{green}{(x)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{4}{7}x+\frac{12}{5}x-\frac{12}{5}.\frac{4}{7}& \text{Uitwerken } \\ & =-x^2+(\frac{4}{7}+\frac{12}{5})x-\frac{48}{35} & \text{Neem samen} \\ &=-x^2+\frac{104}{35}x-\frac{48}{35} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{20}{12}+x)(\frac{-13}{15}+q)& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{15}x+\frac{5}{3}q-\frac{5}{3}.\frac{13}{15}& \text{Uitwerken } \\ & =qx-\frac{13}{15}x+\frac{5}{3}q-\frac{65}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{13}{15}x+\frac{5}{3}q-\frac{13}{9} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q-\frac{-5}{9})(\frac{-16}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{5}{9}}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{5}q+\frac{5}{9}a-\frac{5}{9}.\frac{4}{5}& \text{Uitwerken } \\ & =aq-\frac{4}{5}q+\frac{5}{9}a-\frac{20}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{4}{5}q+\frac{5}{9}a-\frac{4}{9} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{1}{8}+a)(b+\frac{-15}{3})& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{b}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-5)} + \color{orange}{(\frac{1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = ab-5a+\frac{1}{8}b-\frac{1}{8}.5& \text{Uitwerken } \\ & =ab-5a+\frac{1}{8}b-\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{18}{10}+p)(\frac{-6}{11}-p)& =(\color{red}{p}+\color{orange}{\frac{9}{5}}).(\color{green}{-p}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{9}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{6}{11}p-\frac{9}{5}p-\frac{9}{5}.\frac{6}{11}& \text{Uitwerken } \\ & =-p^2+((\frac{-6}{11})+(\frac{-9}{5}))p-\frac{54}{55} & \text{Neem samen} \\ &=-p^2-\frac{129}{55}p-\frac{54}{55} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(q-\frac{-1}{20})(b-\frac{3}{15})& =(\color{red}{q}+\color{orange}{\frac{1}{20}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{1}{20})} . \color{green}{(b)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{5}q+\frac{1}{20}b-\frac{1}{20}.\frac{1}{5}& \text{Uitwerken } \\ & =bq-\frac{1}{5}q+\frac{1}{20}b-\frac{1}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{14}{14}+b)(\frac{-7}{14}-a)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{2}b-1a-1.\frac{1}{2}& \text{Uitwerken } \\ & =-ab-\frac{1}{2}b-1a-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)