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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-14}{14}-a)(\frac{1}{19}+p)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{19}a-1p-1.\frac{1}{19}& \text{Uitwerken } \\ & =-ap-\frac{1}{19}a-1p-\frac{1}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-9}{5}+a)(q-2)& =(\color{red}{a}+\color{orange}{\frac{-9}{5}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{-9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aq-2a-\frac{9}{5}q+\frac{9}{5}.2& \text{Uitwerken } \\ & =aq-2a-\frac{9}{5}q+\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{13}{6}+q)(p-\frac{-6}{15})& =(\color{red}{q}+\color{orange}{\frac{13}{6}}).(\color{green}{p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{13}{6})} . \color{green}{(p)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{5}q+\frac{13}{6}p+\frac{13}{6}.\frac{2}{5}& \text{Uitwerken } \\ & =pq+\frac{2}{5}q+\frac{13}{6}p+\frac{26}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{2}{5}q+\frac{13}{6}p+\frac{13}{15} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-15}{4}-a)(b+\frac{16}{3})& =(\color{red}{-a}+\color{orange}{\frac{-15}{4}}).(\color{green}{b}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{16}{3}a-\frac{15}{4}b-\frac{15}{4}.\frac{16}{3}& \text{Uitwerken } \\ & =-ab-\frac{16}{3}a-\frac{15}{4}b-\frac{240}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{16}{3}a-\frac{15}{4}b-20 & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{4}{20}-q)(\frac{-6}{19}+x)& =(\color{red}{-q}+\color{orange}{\frac{1}{5}}).(\color{green}{x}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{6}{19}q+\frac{1}{5}x-\frac{1}{5}.\frac{6}{19}& \text{Uitwerken } \\ & =-qx+\frac{6}{19}q+\frac{1}{5}x-\frac{6}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{12}{2})(b-(-7))& =(\color{red}{q}+\color{orange}{6}).(\color{green}{b}+\color{blue}{7})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(7)} + \color{orange}{(6)} . \color{green}{(b)} + \color{orange}{(6)} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = bq+7q+6b+6.7& \text{Uitwerken } \\ & =bq+7q+6b+42 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{11}{3})(\frac{16}{18}-p)& =(\color{red}{b}+\color{orange}{\frac{11}{3}}).(\color{green}{-p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{11}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{8}{9}b-\frac{11}{3}p+\frac{11}{3}.\frac{8}{9}& \text{Uitwerken } \\ & =-bp+\frac{8}{9}b-\frac{11}{3}p+\frac{88}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{8}{20}+p)(b+\frac{-19}{5})& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{5}p+\frac{2}{5}b-\frac{2}{5}.\frac{19}{5}& \text{Uitwerken } \\ & =bp-\frac{19}{5}p+\frac{2}{5}b-\frac{38}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b-\frac{4}{18})(\frac{-3}{17}+q)& =(\color{red}{b}+\color{orange}{\frac{-2}{9}}).(\color{green}{q}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{17}b-\frac{2}{9}q+\frac{2}{9}.\frac{3}{17}& \text{Uitwerken } \\ & =bq-\frac{3}{17}b-\frac{2}{9}q+\frac{6}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{3}{17}b-\frac{2}{9}q+\frac{2}{51} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-8}{9}-b)(\frac{14}{10}+q)& =(\color{red}{-b}+\color{orange}{\frac{-8}{9}}).(\color{green}{q}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{5}b-\frac{8}{9}q-\frac{8}{9}.\frac{7}{5}& \text{Uitwerken } \\ & =-bq-\frac{7}{5}b-\frac{8}{9}q-\frac{56}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{14}{17}-b)(\frac{-20}{19}+q)& =(\color{red}{-b}+\color{orange}{\frac{14}{17}}).(\color{green}{q}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{14}{17})} . \color{green}{(q)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{20}{19}b+\frac{14}{17}q-\frac{14}{17}.\frac{20}{19}& \text{Uitwerken } \\ & =-bq+\frac{20}{19}b+\frac{14}{17}q-\frac{280}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-20}{15}+q)(\frac{-19}{3}+x)& =(\color{red}{q}+\color{orange}{\frac{-4}{3}}).(\color{green}{x}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{3}q-\frac{4}{3}x+\frac{4}{3}.\frac{19}{3}& \text{Uitwerken } \\ & =qx-\frac{19}{3}q-\frac{4}{3}x+\frac{76}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)