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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{4}{12})(x+\frac{1}{10})& =(\color{red}{q}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{10}q+\frac{1}{3}x+\frac{1}{3}.\frac{1}{10}& \text{Uitwerken } \\ & =qx+\frac{1}{10}q+\frac{1}{3}x+\frac{1}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-8}{14}-q)(q+\frac{-14}{3})& =(\color{red}{-q}+\color{orange}{\frac{-4}{7}}).(\color{green}{q}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{14}{3}q-\frac{4}{7}q+\frac{4}{7}.\frac{14}{3}& \text{Uitwerken } \\ & =-q^2+(\frac{14}{3}+(\frac{-4}{7}))q+(\frac{-56}{21}) & \text{Neem samen} \\ &=-q^2+\frac{86}{21}q+(\frac{-56}{21}) & \text{Maak de som} \\ &=-q^2+\frac{86}{21}q+(\frac{-8}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
3. \(\begin{align}(\frac{-10}{10}-a)(\frac{2}{6}+x)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{3}a-1x-1.\frac{1}{3}& \text{Uitwerken } \\ & =-ax-\frac{1}{3}a-1x-\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{-4}{6})(\frac{7}{7}+a)& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p-\frac{2}{3}a-\frac{2}{3}.1& \text{Uitwerken } \\ & =ap+1p-\frac{2}{3}a-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{11}{11}+p)(x+\frac{-3}{8})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{8}p+1x-1.\frac{3}{8}& \text{Uitwerken } \\ & =px-\frac{3}{8}p+1x-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-\frac{15}{18})(\frac{16}{10}+b)& =(\color{red}{p}+\color{orange}{\frac{-5}{6}}).(\color{green}{b}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{8}{5}p-\frac{5}{6}b-\frac{5}{6}.\frac{8}{5}& \text{Uitwerken } \\ & =bp+\frac{8}{5}p-\frac{5}{6}b-\frac{40}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{8}{5}p-\frac{5}{6}b-\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-13}{12}-q)(b-\frac{-5}{20})& =(\color{red}{-q}+\color{orange}{\frac{-13}{12}}).(\color{green}{b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{4}q-\frac{13}{12}b-\frac{13}{12}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq-\frac{1}{4}q-\frac{13}{12}b-\frac{13}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{2}{19})(\frac{2}{17}-b)& =(\color{red}{p}+\color{orange}{\frac{2}{19}}).(\color{green}{-b}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{2}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{2}{17}p-\frac{2}{19}b+\frac{2}{19}.\frac{2}{17}& \text{Uitwerken } \\ & =-bp+\frac{2}{17}p-\frac{2}{19}b+\frac{4}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-5}{5}+a)(p-\frac{-19}{13})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{13}a-1p-1.\frac{19}{13}& \text{Uitwerken } \\ & =ap+\frac{19}{13}a-1p-\frac{19}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{6}{3})(\frac{10}{10}+x)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = xx+1x-2x-2.1& \text{Uitwerken } \\ & =x^2+(1+(-2))x-(-2) & \text{Neem samen} \\ &=x^2-1x-(-2) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(x-\frac{3}{7})(\frac{2}{18}-q)& =(\color{red}{x}+\color{orange}{\frac{-3}{7}}).(\color{green}{-q}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{9}x+\frac{3}{7}q-\frac{3}{7}.\frac{1}{9}& \text{Uitwerken } \\ & =-qx+\frac{1}{9}x+\frac{3}{7}q-\frac{3}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{1}{9}x+\frac{3}{7}q-\frac{1}{21} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(a-\frac{-10}{7})(\frac{-5}{4}-p)& =(\color{red}{a}+\color{orange}{\frac{10}{7}}).(\color{green}{-p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{4}a-\frac{10}{7}p-\frac{10}{7}.\frac{5}{4}& \text{Uitwerken } \\ & =-ap-\frac{5}{4}a-\frac{10}{7}p-\frac{50}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{5}{4}a-\frac{10}{7}p-\frac{25}{14} & \text{Vereenvoudig} \\\end{align}\)