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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{6}{3}-b)(\frac{13}{18}+q)& =(\color{red}{-b}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{18}b+2q+2.\frac{13}{18}& \text{Uitwerken } \\ & =-bq-\frac{13}{18}b+2q+\frac{26}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{13}{18}b+2q+\frac{13}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(a-\frac{15}{15})(\frac{8}{16}-p)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{2}a+1p-1.\frac{1}{2}& \text{Uitwerken } \\ & =-ap+\frac{1}{2}a+1p-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x+\frac{-17}{10})(\frac{-15}{20}-b)& =(\color{red}{x}+\color{orange}{\frac{-17}{10}}).(\color{green}{-b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{4}x+\frac{17}{10}b+\frac{17}{10}.\frac{3}{4}& \text{Uitwerken } \\ & =-bx-\frac{3}{4}x+\frac{17}{10}b+\frac{51}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p-\frac{-18}{12})(\frac{-17}{19}+q)& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{19}p+\frac{3}{2}q-\frac{3}{2}.\frac{17}{19}& \text{Uitwerken } \\ & =pq-\frac{17}{19}p+\frac{3}{2}q-\frac{51}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+(-19))(q-\frac{2}{11})& =(\color{red}{p}+\color{orange}{(-19)}).(\color{green}{q}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(-19)} . \color{green}{(q)} + \color{orange}{(-19)} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{11}p-19q+19.\frac{2}{11}& \text{Uitwerken } \\ & =pq-\frac{2}{11}p-19q+\frac{38}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-\frac{-13}{17})(p-\frac{-13}{14})& =(\color{red}{a}+\color{orange}{\frac{13}{17}}).(\color{green}{p}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{13}{17})} . \color{green}{(p)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{14}a+\frac{13}{17}p+\frac{13}{17}.\frac{13}{14}& \text{Uitwerken } \\ & =ap+\frac{13}{14}a+\frac{13}{17}p+\frac{169}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{10}{10})(\frac{-13}{8}-x)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{8}b-1x-1.\frac{13}{8}& \text{Uitwerken } \\ & =-bx-\frac{13}{8}b-1x-\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{3}{18})(b+\frac{-17}{10})& =(\color{red}{q}+\color{orange}{\frac{-1}{6}}).(\color{green}{b}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{10}q-\frac{1}{6}b+\frac{1}{6}.\frac{17}{10}& \text{Uitwerken } \\ & =bq-\frac{17}{10}q-\frac{1}{6}b+\frac{17}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{5}{11})(\frac{12}{10}-q)& =(\color{red}{p}+\color{orange}{\frac{-5}{11}}).(\color{green}{-q}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{6}{5}p+\frac{5}{11}q-\frac{5}{11}.\frac{6}{5}& \text{Uitwerken } \\ & =-pq+\frac{6}{5}p+\frac{5}{11}q-\frac{30}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{6}{5}p+\frac{5}{11}q-\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q+\frac{-1}{18})(\frac{-5}{13}+p)& =(\color{red}{q}+\color{orange}{\frac{-1}{18}}).(\color{green}{p}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-1}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{13}q-\frac{1}{18}p+\frac{1}{18}.\frac{5}{13}& \text{Uitwerken } \\ & =pq-\frac{5}{13}q-\frac{1}{18}p+\frac{5}{234} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-1}{11}-a)(\frac{5}{4}-a)& =(\color{red}{-a}+\color{orange}{\frac{-1}{11}}).(\color{green}{-a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{4}a+\frac{1}{11}a-\frac{1}{11}.\frac{5}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{4})+\frac{1}{11})a-(\frac{-5}{44}) & \text{Neem samen} \\ &=a^2-\frac{51}{44}a-(\frac{-5}{44}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{8}{3}+p)(\frac{11}{8}-q)& =(\color{red}{p}+\color{orange}{\frac{8}{3}}).(\color{green}{-q}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{8}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{8}p-\frac{8}{3}q+\frac{8}{3}.\frac{11}{8}& \text{Uitwerken } \\ & =-pq+\frac{11}{8}p-\frac{8}{3}q+\frac{88}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{11}{8}p-\frac{8}{3}q+\frac{11}{3} & \text{Vereenvoudig} \\\end{align}\)