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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-20}{3})(\frac{-20}{14}+x)& =(\color{red}{p}+\color{orange}{\frac{-20}{3}}).(\color{green}{x}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{7}p-\frac{20}{3}x+\frac{20}{3}.\frac{10}{7}& \text{Uitwerken } \\ & =px-\frac{10}{7}p-\frac{20}{3}x+\frac{200}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{6}{7}+x)(q-\frac{-14}{9})& =(\color{red}{x}+\color{orange}{\frac{6}{7}}).(\color{green}{q}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{14}{9}x+\frac{6}{7}q+\frac{6}{7}.\frac{14}{9}& \text{Uitwerken } \\ & =qx+\frac{14}{9}x+\frac{6}{7}q+\frac{84}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{14}{9}x+\frac{6}{7}q+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-14}{20}+q)(x-\frac{-12}{5})& =(\color{red}{q}+\color{orange}{\frac{-7}{10}}).(\color{green}{x}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{5}q-\frac{7}{10}x-\frac{7}{10}.\frac{12}{5}& \text{Uitwerken } \\ & =qx+\frac{12}{5}q-\frac{7}{10}x-\frac{84}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{5}q-\frac{7}{10}x-\frac{42}{25} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-9}{9}-q)(p+\frac{-19}{20})& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{19}{20}q-1p+1.\frac{19}{20}& \text{Uitwerken } \\ & =-pq+\frac{19}{20}q-1p+\frac{19}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-14}{18}-q)(\frac{-14}{14}+b)& =(\color{red}{-q}+\color{orange}{\frac{-7}{9}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-7}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bq+1q-\frac{7}{9}b+\frac{7}{9}.1& \text{Uitwerken } \\ & =-bq+1q-\frac{7}{9}b+\frac{7}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p+\frac{-8}{3})(q+14)& =(\color{red}{p}+\color{orange}{\frac{-8}{3}}).(\color{green}{q}+\color{blue}{14})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(14)} + \color{orange}{(\frac{-8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = pq+14p-\frac{8}{3}q-\frac{8}{3}.14& \text{Uitwerken } \\ & =pq+14p-\frac{8}{3}q-\frac{112}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{-13}{20})(b+\frac{-4}{6})& =(\color{red}{a}+\color{orange}{\frac{13}{20}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{13}{20})} . \color{green}{(b)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{3}a+\frac{13}{20}b-\frac{13}{20}.\frac{2}{3}& \text{Uitwerken } \\ & =ab-\frac{2}{3}a+\frac{13}{20}b-\frac{26}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{2}{3}a+\frac{13}{20}b-\frac{13}{30} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-20}{20}+a)(b-\frac{2}{3})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{3}a-1b+1.\frac{2}{3}& \text{Uitwerken } \\ & =ab-\frac{2}{3}a-1b+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{5}{9})(b-\frac{-20}{18})& =(\color{red}{x}+\color{orange}{\frac{5}{9}}).(\color{green}{b}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{5}{9})} . \color{green}{(b)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{10}{9}x+\frac{5}{9}b+\frac{5}{9}.\frac{10}{9}& \text{Uitwerken } \\ & =bx+\frac{10}{9}x+\frac{5}{9}b+\frac{50}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{18}{10}-q)(10-p)& =(\color{red}{-q}+\color{orange}{\frac{9}{5}}).(\color{green}{-p}+\color{blue}{10})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(10)} + \color{orange}{(\frac{9}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = pq-10q-\frac{9}{5}p+\frac{9}{5}.10& \text{Uitwerken } \\ & =pq-10q-\frac{9}{5}p+\frac{90}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-10q-\frac{9}{5}p+18 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q+\frac{-6}{18})(b-\frac{13}{8})& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{8}q-\frac{1}{3}b+\frac{1}{3}.\frac{13}{8}& \text{Uitwerken } \\ & =bq-\frac{13}{8}q-\frac{1}{3}b+\frac{13}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{19}{15}+b)(\frac{-17}{13}-a)& =(\color{red}{b}+\color{orange}{\frac{19}{15}}).(\color{green}{-a}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{19}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{17}{13}b-\frac{19}{15}a-\frac{19}{15}.\frac{17}{13}& \text{Uitwerken } \\ & =-ab-\frac{17}{13}b-\frac{19}{15}a-\frac{323}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)