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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{17}{16}+a)(q+\frac{10}{8})& =(\color{red}{a}+\color{orange}{\frac{17}{16}}).(\color{green}{q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{17}{16})} . \color{green}{(q)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{4}a+\frac{17}{16}q+\frac{17}{16}.\frac{5}{4}& \text{Uitwerken } \\ & =aq+\frac{5}{4}a+\frac{17}{16}q+\frac{85}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q+\frac{-1}{8})(b-(-1))& =(\color{red}{q}+\color{orange}{\frac{-1}{8}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q-\frac{1}{8}b-\frac{1}{8}.1& \text{Uitwerken } \\ & =bq+1q-\frac{1}{8}b-\frac{1}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-1}{18}-a)(\frac{-14}{10}-x)& =(\color{red}{-a}+\color{orange}{\frac{-1}{18}}).(\color{green}{-x}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-1}{18})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{5}a+\frac{1}{18}x+\frac{1}{18}.\frac{7}{5}& \text{Uitwerken } \\ & =ax+\frac{7}{5}a+\frac{1}{18}x+\frac{7}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-19}{7}-p)(\frac{-18}{9}-q)& =(\color{red}{-p}+\color{orange}{\frac{-19}{7}}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-19}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq+2p+\frac{19}{7}q+\frac{19}{7}.2& \text{Uitwerken } \\ & =pq+2p+\frac{19}{7}q+\frac{38}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-19}{10})((-10)+b)& =(\color{red}{p}+\color{orange}{\frac{-19}{10}}).(\color{green}{b}+\color{blue}{(-10)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-10)} + \color{orange}{(\frac{-19}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = bp-10p-\frac{19}{10}b+\frac{19}{10}.10& \text{Uitwerken } \\ & =bp-10p-\frac{19}{10}b+\frac{190}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-10p-\frac{19}{10}b+19 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{10}{20}-b)(p-\frac{19}{10})& =(\color{red}{-b}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{10}b+\frac{1}{2}p-\frac{1}{2}.\frac{19}{10}& \text{Uitwerken } \\ & =-bp+\frac{19}{10}b+\frac{1}{2}p-\frac{19}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-8}{10}+x)(\frac{-7}{10}-a)& =(\color{red}{x}+\color{orange}{\frac{-4}{5}}).(\color{green}{-a}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{10}x+\frac{4}{5}a+\frac{4}{5}.\frac{7}{10}& \text{Uitwerken } \\ & =-ax-\frac{7}{10}x+\frac{4}{5}a+\frac{28}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{7}{10}x+\frac{4}{5}a+\frac{14}{25} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{19}{9}-q)(p+\frac{18}{3})& =(\color{red}{-q}+\color{orange}{\frac{19}{9}}).(\color{green}{p}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(6)} + \color{orange}{(\frac{19}{9})} . \color{green}{(p)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -pq-6q+\frac{19}{9}p+\frac{19}{9}.6& \text{Uitwerken } \\ & =-pq-6q+\frac{19}{9}p+\frac{114}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-6q+\frac{19}{9}p+\frac{38}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{13}{14}+b)(\frac{8}{12}+q)& =(\color{red}{b}+\color{orange}{\frac{13}{14}}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{13}{14})} . \color{green}{(q)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{3}b+\frac{13}{14}q+\frac{13}{14}.\frac{2}{3}& \text{Uitwerken } \\ & =bq+\frac{2}{3}b+\frac{13}{14}q+\frac{26}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{2}{3}b+\frac{13}{14}q+\frac{13}{21} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{6}{20}-b)(q-\frac{20}{16})& =(\color{red}{-b}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{4}b+\frac{3}{10}q-\frac{3}{10}.\frac{5}{4}& \text{Uitwerken } \\ & =-bq+\frac{5}{4}b+\frac{3}{10}q-\frac{15}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{5}{4}b+\frac{3}{10}q-\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{20}{18}-p)(p-\frac{-1}{11})& =(\color{red}{-p}+\color{orange}{\frac{10}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{10}{9})} . \color{green}{(p)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{11}p+\frac{10}{9}p+\frac{10}{9}.\frac{1}{11}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{11})+\frac{10}{9})p+(\frac{-10}{99}) & \text{Neem samen} \\ &=-p^2+\frac{101}{99}p+(\frac{-10}{99}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(p-\frac{19}{9})(\frac{12}{20}-a)& =(\color{red}{p}+\color{orange}{\frac{-19}{9}}).(\color{green}{-a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{5}p+\frac{19}{9}a-\frac{19}{9}.\frac{3}{5}& \text{Uitwerken } \\ & =-ap+\frac{3}{5}p+\frac{19}{9}a-\frac{57}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{3}{5}p+\frac{19}{9}a-\frac{19}{15} & \text{Vereenvoudig} \\\end{align}\)