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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-20}{6}-a)(x+\frac{18}{4})& =(\color{red}{-a}+\color{orange}{\frac{-10}{3}}).(\color{green}{x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{9}{2}a-\frac{10}{3}x-\frac{10}{3}.\frac{9}{2}& \text{Uitwerken } \\ & =-ax-\frac{9}{2}a-\frac{10}{3}x-\frac{90}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{9}{2}a-\frac{10}{3}x-15 & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x-\frac{8}{12})(\frac{20}{14}-p)& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{-p}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{10}{7}x+\frac{2}{3}p-\frac{2}{3}.\frac{10}{7}& \text{Uitwerken } \\ & =-px+\frac{10}{7}x+\frac{2}{3}p-\frac{20}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{13}{6})(b+\frac{-1}{18})& =(\color{red}{p}+\color{orange}{\frac{-13}{6}}).(\color{green}{b}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{18}p-\frac{13}{6}b+\frac{13}{6}.\frac{1}{18}& \text{Uitwerken } \\ & =bp-\frac{1}{18}p-\frac{13}{6}b+\frac{13}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-17}{9}+b)(\frac{-2}{7}-x)& =(\color{red}{b}+\color{orange}{\frac{-17}{9}}).(\color{green}{-x}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{2}{7}b+\frac{17}{9}x+\frac{17}{9}.\frac{2}{7}& \text{Uitwerken } \\ & =-bx-\frac{2}{7}b+\frac{17}{9}x+\frac{34}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{18}{19}+b)(p-14)& =(\color{red}{b}+\color{orange}{\frac{18}{19}}).(\color{green}{p}+\color{blue}{(-14)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-14)} + \color{orange}{(\frac{18}{19})} . \color{green}{(p)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = bp-14b+\frac{18}{19}p-\frac{18}{19}.14& \text{Uitwerken } \\ & =bp-14b+\frac{18}{19}p-\frac{252}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-19}{10}-q)(p+\frac{10}{19})& =(\color{red}{-q}+\color{orange}{\frac{-19}{10}}).(\color{green}{p}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{-19}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{10}{19}q-\frac{19}{10}p-\frac{19}{10}.\frac{10}{19}& \text{Uitwerken } \\ & =-pq-\frac{10}{19}q-\frac{19}{10}p-\frac{190}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{10}{19}q-\frac{19}{10}p-1 & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q+\frac{18}{11})((-1)-x)& =(\color{red}{q}+\color{orange}{\frac{18}{11}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{18}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx-1q-\frac{18}{11}x-\frac{18}{11}.1& \text{Uitwerken } \\ & =-qx-1q-\frac{18}{11}x-\frac{18}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-15}{3}-a)(q+\frac{19}{20})& =(\color{red}{-a}+\color{orange}{(-5)}).(\color{green}{q}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(-5)} . \color{green}{(q)} + \color{orange}{(-5)} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{20}a-5q-5.\frac{19}{20}& \text{Uitwerken } \\ & =-aq-\frac{19}{20}a-5q-\frac{95}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{19}{20}a-5q-\frac{19}{4} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x-\frac{-14}{10})(q+\frac{19}{10})& =(\color{red}{x}+\color{orange}{\frac{7}{5}}).(\color{green}{q}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{10}x+\frac{7}{5}q+\frac{7}{5}.\frac{19}{10}& \text{Uitwerken } \\ & =qx+\frac{19}{10}x+\frac{7}{5}q+\frac{133}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{10}{4}+b)(\frac{-10}{20}+x)& =(\color{red}{b}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}b+\frac{5}{2}x-\frac{5}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}b+\frac{5}{2}x-\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{2}{4}-x)(\frac{7}{10}+p)& =(\color{red}{-x}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{10}x+\frac{1}{2}p+\frac{1}{2}.\frac{7}{10}& \text{Uitwerken } \\ & =-px-\frac{7}{10}x+\frac{1}{2}p+\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{18}{20}-x)(a-17)& =(\color{red}{-x}+\color{orange}{\frac{9}{10}}).(\color{green}{a}+\color{blue}{(-17)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(-17)} + \color{orange}{(\frac{9}{10})} . \color{green}{(a)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(-17)}& \text{Boogjes en uitschrijven} \\ & = -ax+17x+\frac{9}{10}a-\frac{9}{10}.17& \text{Uitwerken } \\ & =-ax+17x+\frac{9}{10}a-\frac{153}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)