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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{18}{6}+b)(a+\frac{8}{20})& =(\color{red}{b}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{5}b+3a+3.\frac{2}{5}& \text{Uitwerken } \\ & =ab+\frac{2}{5}b+3a+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{-16}{18})(\frac{-7}{19}+a)& =(\color{red}{b}+\color{orange}{\frac{-8}{9}}).(\color{green}{a}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{19}b-\frac{8}{9}a+\frac{8}{9}.\frac{7}{19}& \text{Uitwerken } \\ & =ab-\frac{7}{19}b-\frac{8}{9}a+\frac{56}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{-10}{6})(\frac{-12}{19}-q)& =(\color{red}{q}+\color{orange}{\frac{5}{3}}).(\color{green}{-q}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{12}{19}q-\frac{5}{3}q-\frac{5}{3}.\frac{12}{19}& \text{Uitwerken } \\ & =-q^2+((\frac{-12}{19})+(\frac{-5}{3}))q-\frac{60}{57} & \text{Neem samen} \\ &=-q^2-\frac{131}{57}q-\frac{60}{57} & \text{Maak de som} \\ &=-q^2-\frac{131}{57}q-\frac{20}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(\frac{-16}{9}-x)(x+\frac{-19}{20})& =(\color{red}{-x}+\color{orange}{\frac{-16}{9}}).(\color{green}{x}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{19}{20}x-\frac{16}{9}x+\frac{16}{9}.\frac{19}{20}& \text{Uitwerken } \\ & =-x^2+(\frac{19}{20}+(\frac{-16}{9}))x+(\frac{-304}{180}) & \text{Neem samen} \\ &=-x^2-\frac{149}{180}x+(\frac{-304}{180}) & \text{Maak de som} \\ &=-x^2-\frac{149}{180}x+(\frac{-76}{45}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(\frac{-9}{11}+q)(15+a)& =(\color{red}{q}+\color{orange}{\frac{-9}{11}}).(\color{green}{a}+\color{blue}{15})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(15)} + \color{orange}{(\frac{-9}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(15)}& \text{Boogjes en uitschrijven} \\ & = aq+15q-\frac{9}{11}a-\frac{9}{11}.15& \text{Uitwerken } \\ & =aq+15q-\frac{9}{11}a-\frac{135}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{8}{7}+x)(\frac{9}{14}+x)& =(\color{red}{x}+\color{orange}{\frac{8}{7}}).(\color{green}{x}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{9}{14}x+\frac{8}{7}x+\frac{8}{7}.\frac{9}{14}& \text{Uitwerken } \\ & =x^2+(\frac{9}{14}+\frac{8}{7})x+\frac{72}{98} & \text{Neem samen} \\ &=x^2+\frac{25}{14}x+\frac{72}{98} & \text{Maak de som} \\ &=x^2+\frac{25}{14}x+\frac{36}{49} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(\frac{-3}{4}+x)(\frac{-7}{13}+x)& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{x}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{7}{13}x-\frac{3}{4}x+\frac{3}{4}.\frac{7}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-7}{13})+(\frac{-3}{4}))x+\frac{21}{52} & \text{Neem samen} \\ &=x^2-\frac{67}{52}x+\frac{21}{52} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(a-\frac{17}{5})(\frac{11}{8}-x)& =(\color{red}{a}+\color{orange}{\frac{-17}{5}}).(\color{green}{-x}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{11}{8}a+\frac{17}{5}x-\frac{17}{5}.\frac{11}{8}& \text{Uitwerken } \\ & =-ax+\frac{11}{8}a+\frac{17}{5}x-\frac{187}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{3}{14}+x)(\frac{12}{18}-p)& =(\color{red}{x}+\color{orange}{\frac{3}{14}}).(\color{green}{-p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{3}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{3}x-\frac{3}{14}p+\frac{3}{14}.\frac{2}{3}& \text{Uitwerken } \\ & =-px+\frac{2}{3}x-\frac{3}{14}p+\frac{6}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{2}{3}x-\frac{3}{14}p+\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p+\frac{-9}{8})(\frac{2}{18}+q)& =(\color{red}{p}+\color{orange}{\frac{-9}{8}}).(\color{green}{q}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{9}p-\frac{9}{8}q-\frac{9}{8}.\frac{1}{9}& \text{Uitwerken } \\ & =pq+\frac{1}{9}p-\frac{9}{8}q-\frac{9}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{9}p-\frac{9}{8}q-\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b-\frac{14}{3})(a+\frac{12}{10})& =(\color{red}{b}+\color{orange}{\frac{-14}{3}}).(\color{green}{a}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{6}{5}b-\frac{14}{3}a-\frac{14}{3}.\frac{6}{5}& \text{Uitwerken } \\ & =ab+\frac{6}{5}b-\frac{14}{3}a-\frac{84}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{6}{5}b-\frac{14}{3}a-\frac{28}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q+\frac{12}{8})(p-\frac{6}{19})& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{6}{19}q+\frac{3}{2}p-\frac{3}{2}.\frac{6}{19}& \text{Uitwerken } \\ & =pq-\frac{6}{19}q+\frac{3}{2}p-\frac{18}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{6}{19}q+\frac{3}{2}p-\frac{9}{19} & \text{Vereenvoudig} \\\end{align}\)