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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{16}{9}-q)(\frac{4}{13}-x)& =(\color{red}{-q}+\color{orange}{\frac{16}{9}}).(\color{green}{-x}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{16}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{13}q-\frac{16}{9}x+\frac{16}{9}.\frac{4}{13}& \text{Uitwerken } \\ & =qx-\frac{4}{13}q-\frac{16}{9}x+\frac{64}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{14}{17})(\frac{14}{18}+b)& =(\color{red}{a}+\color{orange}{\frac{14}{17}}).(\color{green}{b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{14}{17})} . \color{green}{(b)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{9}a+\frac{14}{17}b+\frac{14}{17}.\frac{7}{9}& \text{Uitwerken } \\ & =ab+\frac{7}{9}a+\frac{14}{17}b+\frac{98}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(5+a)(\frac{-9}{12}+x)& =(\color{red}{a}+\color{orange}{5}).(\color{green}{x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{4}a+5x-5.\frac{3}{4}& \text{Uitwerken } \\ & =ax-\frac{3}{4}a+5x-\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-18}{5}-x)(\frac{-19}{15}-a)& =(\color{red}{-x}+\color{orange}{\frac{-18}{5}}).(\color{green}{-a}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{15}x+\frac{18}{5}a+\frac{18}{5}.\frac{19}{15}& \text{Uitwerken } \\ & =ax+\frac{19}{15}x+\frac{18}{5}a+\frac{342}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{19}{15}x+\frac{18}{5}a+\frac{114}{25} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-16}{14}-p)(\frac{6}{6}+b)& =(\color{red}{-p}+\color{orange}{\frac{-8}{7}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{-8}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1p-\frac{8}{7}b-\frac{8}{7}.1& \text{Uitwerken } \\ & =-bp-1p-\frac{8}{7}b-\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{7}{2}-a)(x-\frac{2}{11})& =(\color{red}{-a}+\color{orange}{\frac{7}{2}}).(\color{green}{x}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{11}a+\frac{7}{2}x-\frac{7}{2}.\frac{2}{11}& \text{Uitwerken } \\ & =-ax+\frac{2}{11}a+\frac{7}{2}x-\frac{14}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{2}{11}a+\frac{7}{2}x-\frac{7}{11} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-1}{3}-q)(x+\frac{20}{2})& =(\color{red}{-q}+\color{orange}{\frac{-1}{3}}).(\color{green}{x}+\color{blue}{10})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(10)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -qx-10q-\frac{1}{3}x-\frac{1}{3}.10& \text{Uitwerken } \\ & =-qx-10q-\frac{1}{3}x-\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-14}{19}-b)(x+\frac{16}{15})& =(\color{red}{-b}+\color{orange}{\frac{-14}{19}}).(\color{green}{x}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{16}{15}b-\frac{14}{19}x-\frac{14}{19}.\frac{16}{15}& \text{Uitwerken } \\ & =-bx-\frac{16}{15}b-\frac{14}{19}x-\frac{224}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{3}{9})(p+\frac{11}{20})& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{11}{20}p-\frac{1}{3}p-\frac{1}{3}.\frac{11}{20}& \text{Uitwerken } \\ & =p^2+(\frac{11}{20}+(\frac{-1}{3}))p-(\frac{-11}{60}) & \text{Neem samen} \\ &=p^2+\frac{13}{60}p-(\frac{-11}{60}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(x-\frac{20}{18})(a-\frac{7}{18})& =(\color{red}{x}+\color{orange}{\frac{-10}{9}}).(\color{green}{a}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{18}x-\frac{10}{9}a+\frac{10}{9}.\frac{7}{18}& \text{Uitwerken } \\ & =ax-\frac{7}{18}x-\frac{10}{9}a+\frac{70}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{7}{18}x-\frac{10}{9}a+\frac{35}{81} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-7}{8}-b)(a+\frac{9}{15})& =(\color{red}{-b}+\color{orange}{\frac{-7}{8}}).(\color{green}{a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{5}b-\frac{7}{8}a-\frac{7}{8}.\frac{3}{5}& \text{Uitwerken } \\ & =-ab-\frac{3}{5}b-\frac{7}{8}a-\frac{21}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{-17}{8})(a-\frac{12}{2})& =(\color{red}{x}+\color{orange}{\frac{-17}{8}}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-6)} + \color{orange}{(\frac{-17}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ax-6x-\frac{17}{8}a+\frac{17}{8}.6& \text{Uitwerken } \\ & =ax-6x-\frac{17}{8}a+\frac{102}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-6x-\frac{17}{8}a+\frac{51}{4} & \text{Vereenvoudig} \\\end{align}\)