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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{18}{5})(x+\frac{-8}{8})& =(\color{red}{a}+\color{orange}{\frac{18}{5}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{18}{5})} . \color{green}{(x)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a+\frac{18}{5}x-\frac{18}{5}.1& \text{Uitwerken } \\ & =ax-1a+\frac{18}{5}x-\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-7}{9}+q)(x-\frac{3}{4})& =(\color{red}{q}+\color{orange}{\frac{-7}{9}}).(\color{green}{x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{4}q-\frac{7}{9}x+\frac{7}{9}.\frac{3}{4}& \text{Uitwerken } \\ & =qx-\frac{3}{4}q-\frac{7}{9}x+\frac{21}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{3}{4}q-\frac{7}{9}x+\frac{7}{12} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-6}{17}+b)(\frac{17}{19}+q)& =(\color{red}{b}+\color{orange}{\frac{-6}{17}}).(\color{green}{q}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{19}b-\frac{6}{17}q-\frac{6}{17}.\frac{17}{19}& \text{Uitwerken } \\ & =bq+\frac{17}{19}b-\frac{6}{17}q-\frac{102}{323} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{17}{19}b-\frac{6}{17}q-\frac{6}{19} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p-\frac{3}{10})(p-\frac{-14}{2})& =(\color{red}{p}+\color{orange}{\frac{-3}{10}}).(\color{green}{p}+\color{blue}{7})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(7)} + \color{orange}{(\frac{-3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = pp+7p-\frac{3}{10}p-\frac{3}{10}.7& \text{Uitwerken } \\ & =p^2+(7+(\frac{-3}{10}))p-(\frac{-21}{10}) & \text{Neem samen} \\ &=p^2+\frac{67}{10}p-(\frac{-21}{10}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(b-\frac{-4}{5})(q-\frac{8}{13})& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{q}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{13}b+\frac{4}{5}q-\frac{4}{5}.\frac{8}{13}& \text{Uitwerken } \\ & =bq-\frac{8}{13}b+\frac{4}{5}q-\frac{32}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-\frac{7}{8})(b-\frac{-8}{16})& =(\color{red}{a}+\color{orange}{\frac{-7}{8}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a-\frac{7}{8}b-\frac{7}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a-\frac{7}{8}b-\frac{7}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q-\frac{16}{4})(\frac{-12}{6}+x)& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2q-4x+4.2& \text{Uitwerken } \\ & =qx-2q-4x+8 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{7}{20}-p)(p+\frac{7}{16})& =(\color{red}{-p}+\color{orange}{\frac{7}{20}}).(\color{green}{p}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{7}{20})} . \color{green}{(p)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{7}{16}p+\frac{7}{20}p+\frac{7}{20}.\frac{7}{16}& \text{Uitwerken } \\ & =-p^2+((\frac{-7}{16})+\frac{7}{20})p+(\frac{-49}{320}) & \text{Neem samen} \\ &=-p^2-\frac{7}{80}p+(\frac{-49}{320}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(p-\frac{11}{6})(\frac{19}{3}-a)& =(\color{red}{p}+\color{orange}{\frac{-11}{6}}).(\color{green}{-a}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{3}p+\frac{11}{6}a-\frac{11}{6}.\frac{19}{3}& \text{Uitwerken } \\ & =-ap+\frac{19}{3}p+\frac{11}{6}a-\frac{209}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q+\frac{14}{19})(a-(-19))& =(\color{red}{q}+\color{orange}{\frac{14}{19}}).(\color{green}{a}+\color{blue}{19})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(19)} + \color{orange}{(\frac{14}{19})} . \color{green}{(a)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = aq+19q+\frac{14}{19}a+\frac{14}{19}.19& \text{Uitwerken } \\ & =aq+19q+\frac{14}{19}a+\frac{266}{19} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+19q+\frac{14}{19}a+14 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{9}{16}-b)(q-\frac{-15}{13})& =(\color{red}{-b}+\color{orange}{\frac{9}{16}}).(\color{green}{q}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(\frac{9}{16})} . \color{green}{(q)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{15}{13}b+\frac{9}{16}q+\frac{9}{16}.\frac{15}{13}& \text{Uitwerken } \\ & =-bq-\frac{15}{13}b+\frac{9}{16}q+\frac{135}{208} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{1}{15}+p)(\frac{20}{4}+x)& =(\color{red}{p}+\color{orange}{\frac{1}{15}}).(\color{green}{x}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(5)} + \color{orange}{(\frac{1}{15})} . \color{green}{(x)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = px+5p+\frac{1}{15}x+\frac{1}{15}.5& \text{Uitwerken } \\ & =px+5p+\frac{1}{15}x+\frac{5}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+5p+\frac{1}{15}x+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)