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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{6}-x)(\frac{-3}{18}+x)& =(\color{red}{-x}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{6}x-\frac{5}{3}x+\frac{5}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{6}+(\frac{-5}{3}))x+(\frac{-5}{18}) & \text{Neem samen} \\ &=-x^2-\frac{9}{6}x+(\frac{-5}{18}) & \text{Maak de som} \\ &=-x^2-\frac{3}{2}x+(\frac{-5}{18}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(\frac{-19}{10}+x)(a-\frac{-19}{14})& =(\color{red}{x}+\color{orange}{\frac{-19}{10}}).(\color{green}{a}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{-19}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{14}x-\frac{19}{10}a-\frac{19}{10}.\frac{19}{14}& \text{Uitwerken } \\ & =ax+\frac{19}{14}x-\frac{19}{10}a-\frac{361}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{18}{6})(b-\frac{3}{11})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{11}q-3b+3.\frac{3}{11}& \text{Uitwerken } \\ & =bq-\frac{3}{11}q-3b+\frac{9}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-13}{15}-p)(p-\frac{-2}{10})& =(\color{red}{-p}+\color{orange}{\frac{-13}{15}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{5}p-\frac{13}{15}p-\frac{13}{15}.\frac{1}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{5})+(\frac{-13}{15}))p-\frac{13}{75} & \text{Neem samen} \\ &=-p^2-\frac{16}{15}p-\frac{13}{75} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(q-\frac{3}{19})(b+\frac{-14}{4})& =(\color{red}{q}+\color{orange}{\frac{-3}{19}}).(\color{green}{b}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-3}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{2}q-\frac{3}{19}b+\frac{3}{19}.\frac{7}{2}& \text{Uitwerken } \\ & =bq-\frac{7}{2}q-\frac{3}{19}b+\frac{21}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-18}{4}-a)(b-\frac{7}{3})& =(\color{red}{-a}+\color{orange}{\frac{-9}{2}}).(\color{green}{b}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{7}{3}a-\frac{9}{2}b+\frac{9}{2}.\frac{7}{3}& \text{Uitwerken } \\ & =-ab+\frac{7}{3}a-\frac{9}{2}b+\frac{63}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{7}{3}a-\frac{9}{2}b+\frac{21}{2} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-7}{3}-b)(\frac{12}{18}+a)& =(\color{red}{-b}+\color{orange}{\frac{-7}{3}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{3}b-\frac{7}{3}a-\frac{7}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-ab-\frac{2}{3}b-\frac{7}{3}a-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-17}{18}-p)(a+\frac{13}{12})& =(\color{red}{-p}+\color{orange}{\frac{-17}{18}}).(\color{green}{a}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{12}p-\frac{17}{18}a-\frac{17}{18}.\frac{13}{12}& \text{Uitwerken } \\ & =-ap-\frac{13}{12}p-\frac{17}{18}a-\frac{221}{216} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{7}{13}-b)(\frac{6}{17}+b)& =(\color{red}{-b}+\color{orange}{\frac{7}{13}}).(\color{green}{b}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{7}{13})} . \color{green}{(b)} + \color{orange}{(\frac{7}{13})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{6}{17}b+\frac{7}{13}b+\frac{7}{13}.\frac{6}{17}& \text{Uitwerken } \\ & =-b^2+((\frac{-6}{17})+\frac{7}{13})b+(\frac{-42}{221}) & \text{Neem samen} \\ &=-b^2+\frac{41}{221}b+(\frac{-42}{221}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{-12}{6}-a)(b+\frac{-13}{5})& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{13}{5}a-2b+2.\frac{13}{5}& \text{Uitwerken } \\ & =-ab+\frac{13}{5}a-2b+\frac{26}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b+\frac{8}{6})(\frac{-14}{16}-q)& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{-q}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{8}b-\frac{4}{3}q-\frac{4}{3}.\frac{7}{8}& \text{Uitwerken } \\ & =-bq-\frac{7}{8}b-\frac{4}{3}q-\frac{28}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{7}{8}b-\frac{4}{3}q-\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{7}{16}-a)(q+\frac{-11}{18})& =(\color{red}{-a}+\color{orange}{\frac{7}{16}}).(\color{green}{q}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{7}{16})} . \color{green}{(q)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{11}{18}a+\frac{7}{16}q-\frac{7}{16}.\frac{11}{18}& \text{Uitwerken } \\ & =-aq+\frac{11}{18}a+\frac{7}{16}q-\frac{77}{288} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)