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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-\frac{-1}{18})(b+\frac{-20}{3})& =(\color{red}{x}+\color{orange}{\frac{1}{18}}).(\color{green}{b}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{1}{18})} . \color{green}{(b)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{20}{3}x+\frac{1}{18}b-\frac{1}{18}.\frac{20}{3}& \text{Uitwerken } \\ & =bx-\frac{20}{3}x+\frac{1}{18}b-\frac{20}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{20}{3}x+\frac{1}{18}b-\frac{10}{27} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p-\frac{-14}{14})(a-\frac{-14}{18})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{9}p+1a+1.\frac{7}{9}& \text{Uitwerken } \\ & =ap+\frac{7}{9}p+1a+\frac{7}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{12}{16}-p)(\frac{18}{18}-a)& =(\color{red}{-p}+\color{orange}{\frac{3}{4}}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap-1p-\frac{3}{4}a+\frac{3}{4}.1& \text{Uitwerken } \\ & =ap-1p-\frac{3}{4}a+\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{3}{13}+q)(x+\frac{-15}{12})& =(\color{red}{q}+\color{orange}{\frac{3}{13}}).(\color{green}{x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{3}{13})} . \color{green}{(x)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{4}q+\frac{3}{13}x-\frac{3}{13}.\frac{5}{4}& \text{Uitwerken } \\ & =qx-\frac{5}{4}q+\frac{3}{13}x-\frac{15}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{1}{4})(\frac{-2}{4}-p)& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{2}a+\frac{1}{4}p+\frac{1}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =-ap-\frac{1}{2}a+\frac{1}{4}p+\frac{1}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{14}{6}+b)(\frac{15}{12}-q)& =(\color{red}{b}+\color{orange}{\frac{7}{3}}).(\color{green}{-q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{7}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{4}b-\frac{7}{3}q+\frac{7}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =-bq+\frac{5}{4}b-\frac{7}{3}q+\frac{35}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{6}{8}-b)(p-\frac{9}{7})& =(\color{red}{-b}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{7}b+\frac{3}{4}p-\frac{3}{4}.\frac{9}{7}& \text{Uitwerken } \\ & =-bp+\frac{9}{7}b+\frac{3}{4}p-\frac{27}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-19}{13}+q)(x+\frac{1}{3})& =(\color{red}{q}+\color{orange}{\frac{-19}{13}}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{3}q-\frac{19}{13}x-\frac{19}{13}.\frac{1}{3}& \text{Uitwerken } \\ & =qx+\frac{1}{3}q-\frac{19}{13}x-\frac{19}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{3}{15})(\frac{8}{10}-q)& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{-q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{4}{5}x+\frac{1}{5}q-\frac{1}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =-qx+\frac{4}{5}x+\frac{1}{5}q-\frac{4}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{1}{7}+b)(\frac{-6}{3}-p)& =(\color{red}{b}+\color{orange}{\frac{1}{7}}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bp-2b-\frac{1}{7}p-\frac{1}{7}.2& \text{Uitwerken } \\ & =-bp-2b-\frac{1}{7}p-\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-16}{5}+b)(q+\frac{13}{10})& =(\color{red}{b}+\color{orange}{\frac{-16}{5}}).(\color{green}{q}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{10}b-\frac{16}{5}q-\frac{16}{5}.\frac{13}{10}& \text{Uitwerken } \\ & =bq+\frac{13}{10}b-\frac{16}{5}q-\frac{208}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{13}{10}b-\frac{16}{5}q-\frac{104}{25} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q+\frac{-7}{17})(\frac{-17}{15}+a)& =(\color{red}{q}+\color{orange}{\frac{-7}{17}}).(\color{green}{a}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{15}q-\frac{7}{17}a+\frac{7}{17}.\frac{17}{15}& \text{Uitwerken } \\ & =aq-\frac{17}{15}q-\frac{7}{17}a+\frac{119}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{17}{15}q-\frac{7}{17}a+\frac{7}{15} & \text{Vereenvoudig} \\\end{align}\)