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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{6}{19}-q)(a+\frac{9}{6})& =(\color{red}{-q}+\color{orange}{\frac{6}{19}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{6}{19})} . \color{green}{(a)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{2}q+\frac{6}{19}a+\frac{6}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =-aq-\frac{3}{2}q+\frac{6}{19}a+\frac{18}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{3}{2}q+\frac{6}{19}a+\frac{9}{19} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(q+\frac{-16}{15})(\frac{-4}{20}-b)& =(\color{red}{q}+\color{orange}{\frac{-16}{15}}).(\color{green}{-b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{5}q+\frac{16}{15}b+\frac{16}{15}.\frac{1}{5}& \text{Uitwerken } \\ & =-bq-\frac{1}{5}q+\frac{16}{15}b+\frac{16}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-7}{5}-b)(p+\frac{15}{18})& =(\color{red}{-b}+\color{orange}{\frac{-7}{5}}).(\color{green}{p}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{5}{6}b-\frac{7}{5}p-\frac{7}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =-bp-\frac{5}{6}b-\frac{7}{5}p-\frac{35}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{5}{6}b-\frac{7}{5}p-\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(a+\frac{8}{20})(q-\frac{6}{12})& =(\color{red}{a}+\color{orange}{\frac{2}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{2}a+\frac{2}{5}q-\frac{2}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =aq-\frac{1}{2}a+\frac{2}{5}q-\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{2}a+\frac{2}{5}q-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{8}{6}+b)(\frac{17}{10}-p)& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{-p}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{10}b-\frac{4}{3}p+\frac{4}{3}.\frac{17}{10}& \text{Uitwerken } \\ & =-bp+\frac{17}{10}b-\frac{4}{3}p+\frac{68}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{17}{10}b-\frac{4}{3}p+\frac{34}{15} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{5}{14}-x)(q+\frac{11}{2})& =(\color{red}{-x}+\color{orange}{\frac{5}{14}}).(\color{green}{q}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{5}{14})} . \color{green}{(q)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{11}{2}x+\frac{5}{14}q+\frac{5}{14}.\frac{11}{2}& \text{Uitwerken } \\ & =-qx-\frac{11}{2}x+\frac{5}{14}q+\frac{55}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-14}{15}-b)(\frac{9}{19}+x)& =(\color{red}{-b}+\color{orange}{\frac{-14}{15}}).(\color{green}{x}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{9}{19}b-\frac{14}{15}x-\frac{14}{15}.\frac{9}{19}& \text{Uitwerken } \\ & =-bx-\frac{9}{19}b-\frac{14}{15}x-\frac{126}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{9}{19}b-\frac{14}{15}x-\frac{42}{95} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x-\frac{-3}{16})(p+\frac{-17}{20})& =(\color{red}{x}+\color{orange}{\frac{3}{16}}).(\color{green}{p}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{3}{16})} . \color{green}{(p)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{20}x+\frac{3}{16}p-\frac{3}{16}.\frac{17}{20}& \text{Uitwerken } \\ & =px-\frac{17}{20}x+\frac{3}{16}p-\frac{51}{320} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p+\frac{-12}{11})(a+\frac{-8}{3})& =(\color{red}{p}+\color{orange}{\frac{-12}{11}}).(\color{green}{a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{3}p-\frac{12}{11}a+\frac{12}{11}.\frac{8}{3}& \text{Uitwerken } \\ & =ap-\frac{8}{3}p-\frac{12}{11}a+\frac{96}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{8}{3}p-\frac{12}{11}a+\frac{32}{11} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-20}{12}+a)(p-\frac{-12}{2})& =(\color{red}{a}+\color{orange}{\frac{-5}{3}}).(\color{green}{p}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = ap+6a-\frac{5}{3}p-\frac{5}{3}.6& \text{Uitwerken } \\ & =ap+6a-\frac{5}{3}p-\frac{30}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+6a-\frac{5}{3}p-10 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-14}{20}+a)(\frac{17}{11}-a)& =(\color{red}{a}+\color{orange}{\frac{-7}{10}}).(\color{green}{-a}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{17}{11}a+\frac{7}{10}a-\frac{7}{10}.\frac{17}{11}& \text{Uitwerken } \\ & =-a^2+(\frac{17}{11}+\frac{7}{10})a-\frac{119}{110} & \text{Neem samen} \\ &=-a^2+\frac{247}{110}a-\frac{119}{110} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(q+\frac{-20}{8})(\frac{11}{3}+p)& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{3}q-\frac{5}{2}p-\frac{5}{2}.\frac{11}{3}& \text{Uitwerken } \\ & =pq+\frac{11}{3}q-\frac{5}{2}p-\frac{55}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)