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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-19}{20})(\frac{-8}{17}-b)& =(\color{red}{q}+\color{orange}{\frac{19}{20}}).(\color{green}{-b}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{19}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{8}{17}q-\frac{19}{20}b-\frac{19}{20}.\frac{8}{17}& \text{Uitwerken } \\ & =-bq-\frac{8}{17}q-\frac{19}{20}b-\frac{152}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{8}{17}q-\frac{19}{20}b-\frac{38}{85} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p-\frac{17}{10})(\frac{-7}{7}-q)& =(\color{red}{p}+\color{orange}{\frac{-17}{10}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-17}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pq-1p+\frac{17}{10}q+\frac{17}{10}.1& \text{Uitwerken } \\ & =-pq-1p+\frac{17}{10}q+\frac{17}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{-3}{11})(b+\frac{6}{7})& =(\color{red}{b}+\color{orange}{\frac{3}{11}}).(\color{green}{b}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{3}{11})} . \color{green}{(b)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{6}{7}b+\frac{3}{11}b+\frac{3}{11}.\frac{6}{7}& \text{Uitwerken } \\ & =b^2+(\frac{6}{7}+\frac{3}{11})b+\frac{18}{77} & \text{Neem samen} \\ &=b^2+\frac{87}{77}b+\frac{18}{77} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{10}{3}+p)(a+\frac{16}{5})& =(\color{red}{p}+\color{orange}{\frac{10}{3}}).(\color{green}{a}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{5}p+\frac{10}{3}a+\frac{10}{3}.\frac{16}{5}& \text{Uitwerken } \\ & =ap+\frac{16}{5}p+\frac{10}{3}a+\frac{160}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{16}{5}p+\frac{10}{3}a+\frac{32}{3} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{7}{8}+p)(\frac{8}{8}-x)& =(\color{red}{p}+\color{orange}{\frac{7}{8}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -px+1p-\frac{7}{8}x+\frac{7}{8}.1& \text{Uitwerken } \\ & =-px+1p-\frac{7}{8}x+\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{20}{16})(q+\frac{-11}{8})& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{q}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{8}a+\frac{5}{4}q-\frac{5}{4}.\frac{11}{8}& \text{Uitwerken } \\ & =aq-\frac{11}{8}a+\frac{5}{4}q-\frac{55}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b-\frac{18}{20})(\frac{-13}{3}+b)& =(\color{red}{b}+\color{orange}{\frac{-9}{10}}).(\color{green}{b}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{13}{3}b-\frac{9}{10}b+\frac{9}{10}.\frac{13}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-13}{3})+(\frac{-9}{10}))b+\frac{117}{30} & \text{Neem samen} \\ &=b^2-\frac{157}{30}b+\frac{117}{30} & \text{Maak de som} \\ &=b^2-\frac{157}{30}b+\frac{39}{10} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(q-\frac{-20}{18})(\frac{-2}{9}-p)& =(\color{red}{q}+\color{orange}{\frac{10}{9}}).(\color{green}{-p}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{10}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{9}q-\frac{10}{9}p-\frac{10}{9}.\frac{2}{9}& \text{Uitwerken } \\ & =-pq-\frac{2}{9}q-\frac{10}{9}p-\frac{20}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q+\frac{-16}{8})(\frac{-8}{5}-a)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{-a}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(-2)} . \color{green}{(-a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{8}{5}q+2a+2.\frac{8}{5}& \text{Uitwerken } \\ & =-aq-\frac{8}{5}q+2a+\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(4-a)(\frac{-12}{6}-x)& =(\color{red}{-a}+\color{orange}{4}).(\color{green}{-x}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(-2)} + \color{orange}{(4)} . \color{green}{(-x)} + \color{orange}{(4)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ax+2a-4x-4.2& \text{Uitwerken } \\ & =ax+2a-4x-8 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-8}{19}+p)(\frac{7}{11}+q)& =(\color{red}{p}+\color{orange}{\frac{-8}{19}}).(\color{green}{q}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{11}p-\frac{8}{19}q-\frac{8}{19}.\frac{7}{11}& \text{Uitwerken } \\ & =pq+\frac{7}{11}p-\frac{8}{19}q-\frac{56}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p-\frac{-19}{14})(\frac{11}{6}+b)& =(\color{red}{p}+\color{orange}{\frac{19}{14}}).(\color{green}{b}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{19}{14})} . \color{green}{(b)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{6}p+\frac{19}{14}b+\frac{19}{14}.\frac{11}{6}& \text{Uitwerken } \\ & =bp+\frac{11}{6}p+\frac{19}{14}b+\frac{209}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)