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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{17}{18})(\frac{-16}{14}-a)& =(\color{red}{q}+\color{orange}{\frac{17}{18}}).(\color{green}{-a}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{17}{18})} . \color{green}{(-a)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{8}{7}q-\frac{17}{18}a-\frac{17}{18}.\frac{8}{7}& \text{Uitwerken } \\ & =-aq-\frac{8}{7}q-\frac{17}{18}a-\frac{136}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{8}{7}q-\frac{17}{18}a-\frac{68}{63} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-1}{3}+p)(q-\frac{5}{4})& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{4}p-\frac{1}{3}q+\frac{1}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =pq-\frac{5}{4}p-\frac{1}{3}q+\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{-8}{12})(\frac{-13}{13}-x)& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bx-1b+\frac{2}{3}x+\frac{2}{3}.1& \text{Uitwerken } \\ & =-bx-1b+\frac{2}{3}x+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-\frac{13}{6})(x+\frac{-13}{12})& =(\color{red}{b}+\color{orange}{\frac{-13}{6}}).(\color{green}{x}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{12}b-\frac{13}{6}x+\frac{13}{6}.\frac{13}{12}& \text{Uitwerken } \\ & =bx-\frac{13}{12}b-\frac{13}{6}x+\frac{169}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-7}{3}+x)(\frac{-19}{9}-q)& =(\color{red}{x}+\color{orange}{\frac{-7}{3}}).(\color{green}{-q}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{9}x+\frac{7}{3}q+\frac{7}{3}.\frac{19}{9}& \text{Uitwerken } \\ & =-qx-\frac{19}{9}x+\frac{7}{3}q+\frac{133}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{13}{19}-p)(\frac{-11}{17}-b)& =(\color{red}{-p}+\color{orange}{\frac{13}{19}}).(\color{green}{-b}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{13}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{17}p-\frac{13}{19}b-\frac{13}{19}.\frac{11}{17}& \text{Uitwerken } \\ & =bp+\frac{11}{17}p-\frac{13}{19}b-\frac{143}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{7}{2}-x)(\frac{7}{18}+b)& =(\color{red}{-x}+\color{orange}{\frac{7}{2}}).(\color{green}{b}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{7}{18}x+\frac{7}{2}b+\frac{7}{2}.\frac{7}{18}& \text{Uitwerken } \\ & =-bx-\frac{7}{18}x+\frac{7}{2}b+\frac{49}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{19}{15}+x)(\frac{18}{9}+a)& =(\color{red}{x}+\color{orange}{\frac{19}{15}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{19}{15})} . \color{green}{(a)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2x+\frac{19}{15}a+\frac{19}{15}.2& \text{Uitwerken } \\ & =ax+2x+\frac{19}{15}a+\frac{38}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b+\frac{16}{7})(\frac{-18}{17}-x)& =(\color{red}{b}+\color{orange}{\frac{16}{7}}).(\color{green}{-x}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{16}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{18}{17}b-\frac{16}{7}x-\frac{16}{7}.\frac{18}{17}& \text{Uitwerken } \\ & =-bx-\frac{18}{17}b-\frac{16}{7}x-\frac{288}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{17}{11}-q)(\frac{-10}{15}-q)& =(\color{red}{-q}+\color{orange}{\frac{17}{11}}).(\color{green}{-q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{17}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{2}{3}q-\frac{17}{11}q-\frac{17}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =q^2+(\frac{2}{3}+(\frac{-17}{11}))q-(\frac{-34}{33}) & \text{Neem samen} \\ &=q^2-\frac{29}{33}q-(\frac{-34}{33}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-10}{10}-b)(8+q)& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{8})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(8)} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = -bq-8b-1q-1.8& \text{Uitwerken } \\ & =-bq-8b-1q-8 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{2}{16})(x+\frac{11}{15})& =(\color{red}{p}+\color{orange}{\frac{1}{8}}).(\color{green}{x}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{1}{8})} . \color{green}{(x)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{15}p+\frac{1}{8}x+\frac{1}{8}.\frac{11}{15}& \text{Uitwerken } \\ & =px+\frac{11}{15}p+\frac{1}{8}x+\frac{11}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)