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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-17}{4})(q+\frac{-12}{15})& =(\color{red}{p}+\color{orange}{\frac{17}{4}}).(\color{green}{q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{17}{4})} . \color{green}{(q)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{5}p+\frac{17}{4}q-\frac{17}{4}.\frac{4}{5}& \text{Uitwerken } \\ & =pq-\frac{4}{5}p+\frac{17}{4}q-\frac{68}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{4}{5}p+\frac{17}{4}q-\frac{17}{5} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-18}{2}-b)(b-\frac{1}{20})& =(\color{red}{-b}+\color{orange}{(-9)}).(\color{green}{b}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(-9)} . \color{green}{(b)} + \color{orange}{(-9)} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{20}b-9b+9.\frac{1}{20}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{20}+(-9))b+(\frac{-9}{20}) & \text{Neem samen} \\ &=-b^2-\frac{179}{20}b+(\frac{-9}{20}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(p+\frac{-17}{20})(\frac{-2}{6}+x)& =(\color{red}{p}+\color{orange}{\frac{-17}{20}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{3}p-\frac{17}{20}x+\frac{17}{20}.\frac{1}{3}& \text{Uitwerken } \\ & =px-\frac{1}{3}p-\frac{17}{20}x+\frac{17}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{16}{18}-b)(p+\frac{-5}{5})& =(\color{red}{-b}+\color{orange}{\frac{8}{9}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(\frac{8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1b+\frac{8}{9}p-\frac{8}{9}.1& \text{Uitwerken } \\ & =-bp+1b+\frac{8}{9}p-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{13}{4}+q)(a+\frac{-12}{9})& =(\color{red}{q}+\color{orange}{\frac{13}{4}}).(\color{green}{a}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{13}{4})} . \color{green}{(a)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{3}q+\frac{13}{4}a-\frac{13}{4}.\frac{4}{3}& \text{Uitwerken } \\ & =aq-\frac{4}{3}q+\frac{13}{4}a-\frac{52}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{4}{3}q+\frac{13}{4}a-\frac{13}{3} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x-\frac{19}{6})(b+\frac{14}{12})& =(\color{red}{x}+\color{orange}{\frac{-19}{6}}).(\color{green}{b}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{6}x-\frac{19}{6}b-\frac{19}{6}.\frac{7}{6}& \text{Uitwerken } \\ & =bx+\frac{7}{6}x-\frac{19}{6}b-\frac{133}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}((-1)-p)(\frac{16}{11}+a)& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{16}{11}p-1a-1.\frac{16}{11}& \text{Uitwerken } \\ & =-ap-\frac{16}{11}p-1a-\frac{16}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{14}{2}+x)(q-\frac{-1}{15})& =(\color{red}{x}+\color{orange}{7}).(\color{green}{q}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(7)} . \color{green}{(q)} + \color{orange}{(7)} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{15}x+7q+7.\frac{1}{15}& \text{Uitwerken } \\ & =qx+\frac{1}{15}x+7q+\frac{7}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q-\frac{-14}{15})(\frac{-5}{12}-b)& =(\color{red}{q}+\color{orange}{\frac{14}{15}}).(\color{green}{-b}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{14}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{12}q-\frac{14}{15}b-\frac{14}{15}.\frac{5}{12}& \text{Uitwerken } \\ & =-bq-\frac{5}{12}q-\frac{14}{15}b-\frac{70}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{5}{12}q-\frac{14}{15}b-\frac{7}{18} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a+\frac{4}{5})(\frac{17}{13}+b)& =(\color{red}{a}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{13}a+\frac{4}{5}b+\frac{4}{5}.\frac{17}{13}& \text{Uitwerken } \\ & =ab+\frac{17}{13}a+\frac{4}{5}b+\frac{68}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{20}{11}-b)(q+\frac{-17}{18})& =(\color{red}{-b}+\color{orange}{\frac{20}{11}}).(\color{green}{q}+\color{blue}{\frac{-17}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{18})} + \color{orange}{(\frac{20}{11})} . \color{green}{(q)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{-17}{18})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{17}{18}b+\frac{20}{11}q-\frac{20}{11}.\frac{17}{18}& \text{Uitwerken } \\ & =-bq+\frac{17}{18}b+\frac{20}{11}q-\frac{340}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{17}{18}b+\frac{20}{11}q-\frac{170}{99} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{13}{3}-a)(q-(-4))& =(\color{red}{-a}+\color{orange}{\frac{13}{3}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(4)} + \color{orange}{(\frac{13}{3})} . \color{green}{(q)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -aq-4a+\frac{13}{3}q+\frac{13}{3}.4& \text{Uitwerken } \\ & =-aq-4a+\frac{13}{3}q+\frac{52}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)