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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{15}{2}+p)(q+\frac{2}{16})& =(\color{red}{p}+\color{orange}{\frac{15}{2}}).(\color{green}{q}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{15}{2})} . \color{green}{(q)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{8}p+\frac{15}{2}q+\frac{15}{2}.\frac{1}{8}& \text{Uitwerken } \\ & =pq+\frac{1}{8}p+\frac{15}{2}q+\frac{15}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{20}{4}-q)(\frac{-11}{7}-x)& =(\color{red}{-q}+\color{orange}{5}).(\color{green}{-x}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(5)} . \color{green}{(-x)} + \color{orange}{(5)} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{7}q-5x-5.\frac{11}{7}& \text{Uitwerken } \\ & =qx+\frac{11}{7}q-5x-\frac{55}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{10}{13})(\frac{6}{9}+q)& =(\color{red}{p}+\color{orange}{\frac{-10}{13}}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{3}p-\frac{10}{13}q-\frac{10}{13}.\frac{2}{3}& \text{Uitwerken } \\ & =pq+\frac{2}{3}p-\frac{10}{13}q-\frac{20}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{9}{5})(\frac{-19}{4}-a)& =(\color{red}{p}+\color{orange}{\frac{9}{5}}).(\color{green}{-a}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{9}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{19}{4}p-\frac{9}{5}a-\frac{9}{5}.\frac{19}{4}& \text{Uitwerken } \\ & =-ap-\frac{19}{4}p-\frac{9}{5}a-\frac{171}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{10}{14}-a)(q-\frac{-10}{2})& =(\color{red}{-a}+\color{orange}{\frac{5}{7}}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(5)} + \color{orange}{(\frac{5}{7})} . \color{green}{(q)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -aq-5a+\frac{5}{7}q+\frac{5}{7}.5& \text{Uitwerken } \\ & =-aq-5a+\frac{5}{7}q+\frac{25}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{16}{13})(a-\frac{4}{15})& =(\color{red}{q}+\color{orange}{\frac{16}{13}}).(\color{green}{a}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{16}{13})} . \color{green}{(a)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{15}q+\frac{16}{13}a-\frac{16}{13}.\frac{4}{15}& \text{Uitwerken } \\ & =aq-\frac{4}{15}q+\frac{16}{13}a-\frac{64}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-14}{16}+x)(q-\frac{6}{13})& =(\color{red}{x}+\color{orange}{\frac{-7}{8}}).(\color{green}{q}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{6}{13}x-\frac{7}{8}q+\frac{7}{8}.\frac{6}{13}& \text{Uitwerken } \\ & =qx-\frac{6}{13}x-\frac{7}{8}q+\frac{42}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{6}{13}x-\frac{7}{8}q+\frac{21}{52} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q-15)(x-\frac{-2}{14})& =(\color{red}{q}+\color{orange}{(-15)}).(\color{green}{x}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(-15)} . \color{green}{(x)} + \color{orange}{(-15)} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{7}q-15x-15.\frac{1}{7}& \text{Uitwerken } \\ & =qx+\frac{1}{7}q-15x-\frac{15}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{-13}{14})(\frac{16}{8}+b)& =(\color{red}{x}+\color{orange}{\frac{-13}{14}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-13}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bx+2x-\frac{13}{14}b-\frac{13}{14}.2& \text{Uitwerken } \\ & =bx+2x-\frac{13}{14}b-\frac{26}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+2x-\frac{13}{14}b-\frac{13}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{15}{7}+p)(\frac{-8}{4}-q)& =(\color{red}{p}+\color{orange}{\frac{15}{7}}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{15}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pq-2p-\frac{15}{7}q-\frac{15}{7}.2& \text{Uitwerken } \\ & =-pq-2p-\frac{15}{7}q-\frac{30}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-11}{19}-b)(q+\frac{6}{11})& =(\color{red}{-b}+\color{orange}{\frac{-11}{19}}).(\color{green}{q}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{6}{11}b-\frac{11}{19}q-\frac{11}{19}.\frac{6}{11}& \text{Uitwerken } \\ & =-bq-\frac{6}{11}b-\frac{11}{19}q-\frac{66}{209} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{6}{11}b-\frac{11}{19}q-\frac{6}{19} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x-\frac{-3}{11})(\frac{-15}{5}-a)& =(\color{red}{x}+\color{orange}{\frac{3}{11}}).(\color{green}{-a}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{3}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -ax-3x-\frac{3}{11}a-\frac{3}{11}.3& \text{Uitwerken } \\ & =-ax-3x-\frac{3}{11}a-\frac{9}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)