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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{8}{11})(p+\frac{-14}{5})& =(\color{red}{b}+\color{orange}{\frac{-8}{11}}).(\color{green}{p}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{-8}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{14}{5}b-\frac{8}{11}p+\frac{8}{11}.\frac{14}{5}& \text{Uitwerken } \\ & =bp-\frac{14}{5}b-\frac{8}{11}p+\frac{112}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{-13}{20})(\frac{17}{13}+x)& =(\color{red}{b}+\color{orange}{\frac{13}{20}}).(\color{green}{x}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{13}{20})} . \color{green}{(x)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{13}b+\frac{13}{20}x+\frac{13}{20}.\frac{17}{13}& \text{Uitwerken } \\ & =bx+\frac{17}{13}b+\frac{13}{20}x+\frac{221}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{17}{13}b+\frac{13}{20}x+\frac{17}{20} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b+\frac{7}{4})(x-2)& =(\color{red}{b}+\color{orange}{\frac{7}{4}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{7}{4})} . \color{green}{(x)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bx-2b+\frac{7}{4}x-\frac{7}{4}.2& \text{Uitwerken } \\ & =bx-2b+\frac{7}{4}x-\frac{14}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-2b+\frac{7}{4}x-\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{16}{10}-p)(\frac{19}{4}+a)& =(\color{red}{-p}+\color{orange}{\frac{8}{5}}).(\color{green}{a}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{19}{4}p+\frac{8}{5}a+\frac{8}{5}.\frac{19}{4}& \text{Uitwerken } \\ & =-ap-\frac{19}{4}p+\frac{8}{5}a+\frac{152}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{19}{4}p+\frac{8}{5}a+\frac{38}{5} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x-\frac{-7}{11})(q+\frac{-13}{18})& =(\color{red}{x}+\color{orange}{\frac{7}{11}}).(\color{green}{q}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{7}{11})} . \color{green}{(q)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{18}x+\frac{7}{11}q-\frac{7}{11}.\frac{13}{18}& \text{Uitwerken } \\ & =qx-\frac{13}{18}x+\frac{7}{11}q-\frac{91}{198} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{20}{20})(p+\frac{2}{13})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{13}q+1p+1.\frac{2}{13}& \text{Uitwerken } \\ & =pq+\frac{2}{13}q+1p+\frac{2}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{19}{4})(a+\frac{8}{19})& =(\color{red}{p}+\color{orange}{\frac{19}{4}}).(\color{green}{a}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{19}{4})} . \color{green}{(a)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{19}p+\frac{19}{4}a+\frac{19}{4}.\frac{8}{19}& \text{Uitwerken } \\ & =ap+\frac{8}{19}p+\frac{19}{4}a+\frac{152}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{8}{19}p+\frac{19}{4}a+2 & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q+\frac{3}{7})(q+\frac{14}{10})& =(\color{red}{q}+\color{orange}{\frac{3}{7}}).(\color{green}{q}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{5}q+\frac{3}{7}q+\frac{3}{7}.\frac{7}{5}& \text{Uitwerken } \\ & =q^2+(\frac{7}{5}+\frac{3}{7})q+\frac{21}{35} & \text{Neem samen} \\ &=q^2+\frac{64}{35}q+\frac{21}{35} & \text{Maak de som} \\ &=q^2+\frac{64}{35}q+\frac{3}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(a+\frac{7}{19})(\frac{-16}{5}-x)& =(\color{red}{a}+\color{orange}{\frac{7}{19}}).(\color{green}{-x}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{7}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{16}{5}a-\frac{7}{19}x-\frac{7}{19}.\frac{16}{5}& \text{Uitwerken } \\ & =-ax-\frac{16}{5}a-\frac{7}{19}x-\frac{112}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{8}{11}+q)(a-\frac{13}{12})& =(\color{red}{q}+\color{orange}{\frac{8}{11}}).(\color{green}{a}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{8}{11})} . \color{green}{(a)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{12}q+\frac{8}{11}a-\frac{8}{11}.\frac{13}{12}& \text{Uitwerken } \\ & =aq-\frac{13}{12}q+\frac{8}{11}a-\frac{104}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{13}{12}q+\frac{8}{11}a-\frac{26}{33} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q+\frac{-8}{14})(b-\frac{6}{5})& =(\color{red}{q}+\color{orange}{\frac{-4}{7}}).(\color{green}{b}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{6}{5}q-\frac{4}{7}b+\frac{4}{7}.\frac{6}{5}& \text{Uitwerken } \\ & =bq-\frac{6}{5}q-\frac{4}{7}b+\frac{24}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{6}{13}-a)(a+\frac{-20}{4})& =(\color{red}{-a}+\color{orange}{\frac{6}{13}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(-5)} + \color{orange}{(\frac{6}{13})} . \color{green}{(a)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -aa+5a+\frac{6}{13}a-\frac{6}{13}.5& \text{Uitwerken } \\ & =-a^2+(5+\frac{6}{13})a-\frac{30}{13} & \text{Neem samen} \\ &=-a^2+\frac{71}{13}a-\frac{30}{13} & \text{Maak de som} \\\end{align}\)