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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{20}{14}-q)(a-\frac{-2}{17})& =(\color{red}{-q}+\color{orange}{\frac{10}{7}}).(\color{green}{a}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{2}{17}q+\frac{10}{7}a+\frac{10}{7}.\frac{2}{17}& \text{Uitwerken } \\ & =-aq-\frac{2}{17}q+\frac{10}{7}a+\frac{20}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{13}{9}+p)(p-\frac{11}{12})& =(\color{red}{p}+\color{orange}{\frac{13}{9}}).(\color{green}{p}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{13}{9})} . \color{green}{(p)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{11}{12}p+\frac{13}{9}p-\frac{13}{9}.\frac{11}{12}& \text{Uitwerken } \\ & =p^2+((\frac{-11}{12})+\frac{13}{9})p-(\frac{-143}{108}) & \text{Neem samen} \\ &=p^2+\frac{19}{36}p-(\frac{-143}{108}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(17+x)(14-p)& =(\color{red}{x}+\color{orange}{17}).(\color{green}{-p}+\color{blue}{14})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(14)} + \color{orange}{(17)} . \color{green}{(-p)} + \color{orange}{(17)} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = -px+14x-17p+17.14& \text{Uitwerken } \\ & =-px+14x-17p+238 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-20}{8}-q)(b+\frac{5}{16})& =(\color{red}{-q}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{16}q-\frac{5}{2}b-\frac{5}{2}.\frac{5}{16}& \text{Uitwerken } \\ & =-bq-\frac{5}{16}q-\frac{5}{2}b-\frac{25}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{18}{14}+a)(\frac{7}{6}+x)& =(\color{red}{a}+\color{orange}{\frac{9}{7}}).(\color{green}{x}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{9}{7})} . \color{green}{(x)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{6}a+\frac{9}{7}x+\frac{9}{7}.\frac{7}{6}& \text{Uitwerken } \\ & =ax+\frac{7}{6}a+\frac{9}{7}x+\frac{63}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{7}{6}a+\frac{9}{7}x+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-2}{19}-a)(\frac{13}{13}-p)& =(\color{red}{-a}+\color{orange}{\frac{-2}{19}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(1)} + \color{orange}{(\frac{-2}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a+\frac{2}{19}p-\frac{2}{19}.1& \text{Uitwerken } \\ & =ap-1a+\frac{2}{19}p-\frac{2}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{-10}{16})(\frac{16}{11}+b)& =(\color{red}{x}+\color{orange}{\frac{-5}{8}}).(\color{green}{b}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{16}{11}x-\frac{5}{8}b-\frac{5}{8}.\frac{16}{11}& \text{Uitwerken } \\ & =bx+\frac{16}{11}x-\frac{5}{8}b-\frac{80}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{16}{11}x-\frac{5}{8}b-\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x+\frac{-1}{16})(\frac{-16}{12}+q)& =(\color{red}{x}+\color{orange}{\frac{-1}{16}}).(\color{green}{q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{3}x-\frac{1}{16}q+\frac{1}{16}.\frac{4}{3}& \text{Uitwerken } \\ & =qx-\frac{4}{3}x-\frac{1}{16}q+\frac{4}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{4}{3}x-\frac{1}{16}q+\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{16}{7}+x)(b-\frac{-8}{2})& =(\color{red}{x}+\color{orange}{\frac{16}{7}}).(\color{green}{b}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(4)} + \color{orange}{(\frac{16}{7})} . \color{green}{(b)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bx+4x+\frac{16}{7}b+\frac{16}{7}.4& \text{Uitwerken } \\ & =bx+4x+\frac{16}{7}b+\frac{64}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b+15)(\frac{12}{6}+x)& =(\color{red}{b}+\color{orange}{15}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(15)} . \color{green}{(x)} + \color{orange}{(15)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bx+2b+15x+15.2& \text{Uitwerken } \\ & =bx+2b+15x+30 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-9}{6}+x)(\frac{-6}{15}+p)& =(\color{red}{x}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{5}x-\frac{3}{2}p+\frac{3}{2}.\frac{2}{5}& \text{Uitwerken } \\ & =px-\frac{2}{5}x-\frac{3}{2}p+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{2}{5}x-\frac{3}{2}p+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-2}{5}-a)(p+\frac{8}{4})& =(\color{red}{-a}+\color{orange}{\frac{-2}{5}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ap-2a-\frac{2}{5}p-\frac{2}{5}.2& \text{Uitwerken } \\ & =-ap-2a-\frac{2}{5}p-\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)