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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-8}{7})(x+\frac{-19}{4})& =(\color{red}{p}+\color{orange}{\frac{-8}{7}}).(\color{green}{x}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{4}p-\frac{8}{7}x+\frac{8}{7}.\frac{19}{4}& \text{Uitwerken } \\ & =px-\frac{19}{4}p-\frac{8}{7}x+\frac{152}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{19}{4}p-\frac{8}{7}x+\frac{38}{7} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x+\frac{14}{19})(a+\frac{-14}{14})& =(\color{red}{x}+\color{orange}{\frac{14}{19}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{14}{19})} . \color{green}{(a)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x+\frac{14}{19}a-\frac{14}{19}.1& \text{Uitwerken } \\ & =ax-1x+\frac{14}{19}a-\frac{14}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+\frac{-8}{18})(a+\frac{16}{18})& =(\color{red}{q}+\color{orange}{\frac{-4}{9}}).(\color{green}{a}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{9}q-\frac{4}{9}a-\frac{4}{9}.\frac{8}{9}& \text{Uitwerken } \\ & =aq+\frac{8}{9}q-\frac{4}{9}a-\frac{32}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{6}{2})(b-\frac{16}{6})& =(\color{red}{x}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{8}{3}x+3b-3.\frac{8}{3}& \text{Uitwerken } \\ & =bx-\frac{8}{3}x+3b-\frac{24}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{8}{3}x+3b-8 & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(q+\frac{-20}{20})(\frac{20}{13}-b)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{20}{13}q+1b-1.\frac{20}{13}& \text{Uitwerken } \\ & =-bq+\frac{20}{13}q+1b-\frac{20}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-20}{5}-b)(q+\frac{-10}{15})& =(\color{red}{-b}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{3}b-4q+4.\frac{2}{3}& \text{Uitwerken } \\ & =-bq+\frac{2}{3}b-4q+\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q-\frac{-15}{19})(\frac{11}{13}+b)& =(\color{red}{q}+\color{orange}{\frac{15}{19}}).(\color{green}{b}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{15}{19})} . \color{green}{(b)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{13}q+\frac{15}{19}b+\frac{15}{19}.\frac{11}{13}& \text{Uitwerken } \\ & =bq+\frac{11}{13}q+\frac{15}{19}b+\frac{165}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-19}{5}+q)(b-\frac{-13}{6})& =(\color{red}{q}+\color{orange}{\frac{-19}{5}}).(\color{green}{b}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{6}q-\frac{19}{5}b-\frac{19}{5}.\frac{13}{6}& \text{Uitwerken } \\ & =bq+\frac{13}{6}q-\frac{19}{5}b-\frac{247}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{20}{14}+b)(\frac{10}{20}-a)& =(\color{red}{b}+\color{orange}{\frac{10}{7}}).(\color{green}{-a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{2}b-\frac{10}{7}a+\frac{10}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =-ab+\frac{1}{2}b-\frac{10}{7}a+\frac{10}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{1}{2}b-\frac{10}{7}a+\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q+\frac{-8}{4})(\frac{7}{3}+a)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{3}q-2a-2.\frac{7}{3}& \text{Uitwerken } \\ & =aq+\frac{7}{3}q-2a-\frac{14}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{8}{7}-q)(\frac{20}{5}-b)& =(\color{red}{-q}+\color{orange}{\frac{8}{7}}).(\color{green}{-b}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(4)} + \color{orange}{(\frac{8}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bq-4q-\frac{8}{7}b+\frac{8}{7}.4& \text{Uitwerken } \\ & =bq-4q-\frac{8}{7}b+\frac{32}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{-3}{17})(\frac{9}{7}+a)& =(\color{red}{b}+\color{orange}{\frac{-3}{17}}).(\color{green}{a}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-3}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{7}b-\frac{3}{17}a-\frac{3}{17}.\frac{9}{7}& \text{Uitwerken } \\ & =ab+\frac{9}{7}b-\frac{3}{17}a-\frac{27}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)