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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-8}{3})(x+\frac{7}{14})& =(\color{red}{b}+\color{orange}{\frac{-8}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}b-\frac{8}{3}x-\frac{8}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}b-\frac{8}{3}x-\frac{8}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{1}{2}b-\frac{8}{3}x-\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-17}{9}-x)(\frac{16}{16}+q)& =(\color{red}{-x}+\color{orange}{\frac{-17}{9}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{-17}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qx-1x-\frac{17}{9}q-\frac{17}{9}.1& \text{Uitwerken } \\ & =-qx-1x-\frac{17}{9}q-\frac{17}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a-\frac{-18}{11})(q-\frac{19}{20})& =(\color{red}{a}+\color{orange}{\frac{18}{11}}).(\color{green}{q}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{18}{11})} . \color{green}{(q)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{20}a+\frac{18}{11}q-\frac{18}{11}.\frac{19}{20}& \text{Uitwerken } \\ & =aq-\frac{19}{20}a+\frac{18}{11}q-\frac{342}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{19}{20}a+\frac{18}{11}q-\frac{171}{110} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{11}{20}-p)(\frac{9}{2}+x)& =(\color{red}{-p}+\color{orange}{\frac{11}{20}}).(\color{green}{x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{11}{20})} . \color{green}{(x)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{9}{2}p+\frac{11}{20}x+\frac{11}{20}.\frac{9}{2}& \text{Uitwerken } \\ & =-px-\frac{9}{2}p+\frac{11}{20}x+\frac{99}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{-6}{12})(\frac{-7}{15}+b)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{15}a+\frac{1}{2}b-\frac{1}{2}.\frac{7}{15}& \text{Uitwerken } \\ & =ab-\frac{7}{15}a+\frac{1}{2}b-\frac{7}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{-16}{14})(q-\frac{-7}{18})& =(\color{red}{b}+\color{orange}{\frac{-8}{7}}).(\color{green}{q}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{18}b-\frac{8}{7}q-\frac{8}{7}.\frac{7}{18}& \text{Uitwerken } \\ & =bq+\frac{7}{18}b-\frac{8}{7}q-\frac{56}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{7}{18}b-\frac{8}{7}q-\frac{4}{9} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{16}{14}-a)(\frac{4}{10}-p)& =(\color{red}{-a}+\color{orange}{\frac{8}{7}}).(\color{green}{-p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{8}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{5}a-\frac{8}{7}p+\frac{8}{7}.\frac{2}{5}& \text{Uitwerken } \\ & =ap-\frac{2}{5}a-\frac{8}{7}p+\frac{16}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{2}{15}+x)(a-\frac{10}{4})& =(\color{red}{x}+\color{orange}{\frac{2}{15}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{2}{15})} . \color{green}{(a)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{2}x+\frac{2}{15}a-\frac{2}{15}.\frac{5}{2}& \text{Uitwerken } \\ & =ax-\frac{5}{2}x+\frac{2}{15}a-\frac{10}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{2}x+\frac{2}{15}a-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{6}{10}-x)(\frac{5}{5}-x)& =(\color{red}{-x}+\color{orange}{\frac{3}{5}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = xx-1x-\frac{3}{5}x+\frac{3}{5}.1& \text{Uitwerken } \\ & =x^2+((-1)+(\frac{-3}{5}))x+\frac{3}{5} & \text{Neem samen} \\ &=x^2-\frac{8}{5}x+\frac{3}{5} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{7}{12}+p)(\frac{-19}{19}-p)& =(\color{red}{p}+\color{orange}{\frac{7}{12}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pp-1p-\frac{7}{12}p-\frac{7}{12}.1& \text{Uitwerken } \\ & =-p^2+((-1)+(\frac{-7}{12}))p-\frac{7}{12} & \text{Neem samen} \\ &=-p^2-\frac{19}{12}p-\frac{7}{12} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(x-\frac{-17}{8})(\frac{19}{10}-p)& =(\color{red}{x}+\color{orange}{\frac{17}{8}}).(\color{green}{-p}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{17}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{19}{10}x-\frac{17}{8}p+\frac{17}{8}.\frac{19}{10}& \text{Uitwerken } \\ & =-px+\frac{19}{10}x-\frac{17}{8}p+\frac{323}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{-13}{4})(\frac{-20}{4}+a)& =(\color{red}{b}+\color{orange}{\frac{-13}{4}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-5)} + \color{orange}{(\frac{-13}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = ab-5b-\frac{13}{4}a+\frac{13}{4}.5& \text{Uitwerken } \\ & =ab-5b-\frac{13}{4}a+\frac{65}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)