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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{9}{4})(\frac{11}{13}-x)& =(\color{red}{b}+\color{orange}{\frac{9}{4}}).(\color{green}{-x}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{9}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{11}{13}b-\frac{9}{4}x+\frac{9}{4}.\frac{11}{13}& \text{Uitwerken } \\ & =-bx+\frac{11}{13}b-\frac{9}{4}x+\frac{99}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-6}{19}-p)(\frac{-9}{17}-x)& =(\color{red}{-p}+\color{orange}{\frac{-6}{19}}).(\color{green}{-x}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{-6}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{17}p+\frac{6}{19}x+\frac{6}{19}.\frac{9}{17}& \text{Uitwerken } \\ & =px+\frac{9}{17}p+\frac{6}{19}x+\frac{54}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-(-12))(\frac{8}{5}-q)& =(\color{red}{x}+\color{orange}{12}).(\color{green}{-q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(12)} . \color{green}{(-q)} + \color{orange}{(12)} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{8}{5}x-12q+12.\frac{8}{5}& \text{Uitwerken } \\ & =-qx+\frac{8}{5}x-12q+\frac{96}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{19}{16})(a-\frac{7}{20})& =(\color{red}{x}+\color{orange}{\frac{-19}{16}}).(\color{green}{a}+\color{blue}{\frac{-7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{20})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{-7}{20})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{20}x-\frac{19}{16}a+\frac{19}{16}.\frac{7}{20}& \text{Uitwerken } \\ & =ax-\frac{7}{20}x-\frac{19}{16}a+\frac{133}{320} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{6}{8}-b)(\frac{7}{15}-p)& =(\color{red}{-b}+\color{orange}{\frac{3}{4}}).(\color{green}{-p}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{15}b-\frac{3}{4}p+\frac{3}{4}.\frac{7}{15}& \text{Uitwerken } \\ & =bp-\frac{7}{15}b-\frac{3}{4}p+\frac{21}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{7}{15}b-\frac{3}{4}p+\frac{7}{20} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-10}{4}-x)(b-\frac{19}{9})& =(\color{red}{-x}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{19}{9}x-\frac{5}{2}b+\frac{5}{2}.\frac{19}{9}& \text{Uitwerken } \\ & =-bx+\frac{19}{9}x-\frac{5}{2}b+\frac{95}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-6}{18}+q)(b-\frac{-6}{2})& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bq+3q-\frac{1}{3}b-\frac{1}{3}.3& \text{Uitwerken } \\ & =bq+3q-\frac{1}{3}b-\frac{3}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+3q-\frac{1}{3}b-1 & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q-\frac{7}{8})(a+\frac{20}{17})& =(\color{red}{q}+\color{orange}{\frac{-7}{8}}).(\color{green}{a}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{20}{17}q-\frac{7}{8}a-\frac{7}{8}.\frac{20}{17}& \text{Uitwerken } \\ & =aq+\frac{20}{17}q-\frac{7}{8}a-\frac{140}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{20}{17}q-\frac{7}{8}a-\frac{35}{34} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x-\frac{-20}{7})(p+\frac{7}{11})& =(\color{red}{x}+\color{orange}{\frac{20}{7}}).(\color{green}{p}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{20}{7})} . \color{green}{(p)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{11}x+\frac{20}{7}p+\frac{20}{7}.\frac{7}{11}& \text{Uitwerken } \\ & =px+\frac{7}{11}x+\frac{20}{7}p+\frac{140}{77} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{7}{11}x+\frac{20}{7}p+\frac{20}{11} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{14}{10}-p)(p-\frac{3}{17})& =(\color{red}{-p}+\color{orange}{\frac{7}{5}}).(\color{green}{p}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{3}{17}p+\frac{7}{5}p-\frac{7}{5}.\frac{3}{17}& \text{Uitwerken } \\ & =-p^2+(\frac{3}{17}+\frac{7}{5})p-\frac{21}{85} & \text{Neem samen} \\ &=-p^2+\frac{134}{85}p-\frac{21}{85} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(x+\frac{14}{12})(\frac{20}{19}-p)& =(\color{red}{x}+\color{orange}{\frac{7}{6}}).(\color{green}{-p}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{7}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{20}{19}x-\frac{7}{6}p+\frac{7}{6}.\frac{20}{19}& \text{Uitwerken } \\ & =-px+\frac{20}{19}x-\frac{7}{6}p+\frac{140}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{20}{19}x-\frac{7}{6}p+\frac{70}{57} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-3}{3}+a)(\frac{-2}{9}+q)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{9}a-1q+1.\frac{2}{9}& \text{Uitwerken } \\ & =aq-\frac{2}{9}a-1q+\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)