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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{-17}{15})(\frac{11}{2}-x)& =(\color{red}{b}+\color{orange}{\frac{17}{15}}).(\color{green}{-x}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{17}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{11}{2}b-\frac{17}{15}x+\frac{17}{15}.\frac{11}{2}& \text{Uitwerken } \\ & =-bx+\frac{11}{2}b-\frac{17}{15}x+\frac{187}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{17}{4})(\frac{5}{2}-x)& =(\color{red}{a}+\color{orange}{\frac{17}{4}}).(\color{green}{-x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{17}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{2}a-\frac{17}{4}x+\frac{17}{4}.\frac{5}{2}& \text{Uitwerken } \\ & =-ax+\frac{5}{2}a-\frac{17}{4}x+\frac{85}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{19}{4})(q+\frac{-8}{9})& =(\color{red}{p}+\color{orange}{\frac{-19}{4}}).(\color{green}{q}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-19}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{4})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{9}p-\frac{19}{4}q+\frac{19}{4}.\frac{8}{9}& \text{Uitwerken } \\ & =pq-\frac{8}{9}p-\frac{19}{4}q+\frac{152}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{8}{9}p-\frac{19}{4}q+\frac{38}{9} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{1}{17}-x)(b+\frac{-2}{11})& =(\color{red}{-x}+\color{orange}{\frac{1}{17}}).(\color{green}{b}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{1}{17})} . \color{green}{(b)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{2}{11}x+\frac{1}{17}b-\frac{1}{17}.\frac{2}{11}& \text{Uitwerken } \\ & =-bx+\frac{2}{11}x+\frac{1}{17}b-\frac{2}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{2}{9}+x)((-14)+q)& =(\color{red}{x}+\color{orange}{\frac{2}{9}}).(\color{green}{q}+\color{blue}{(-14)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-14)} + \color{orange}{(\frac{2}{9})} . \color{green}{(q)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = qx-14x+\frac{2}{9}q-\frac{2}{9}.14& \text{Uitwerken } \\ & =qx-14x+\frac{2}{9}q-\frac{28}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-16}{12}+x)(\frac{14}{15}+p)& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{14}{15}x-\frac{4}{3}p-\frac{4}{3}.\frac{14}{15}& \text{Uitwerken } \\ & =px+\frac{14}{15}x-\frac{4}{3}p-\frac{56}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-19}{10}+p)(a+\frac{9}{9})& =(\color{red}{p}+\color{orange}{\frac{-19}{10}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p-\frac{19}{10}a-\frac{19}{10}.1& \text{Uitwerken } \\ & =ap+1p-\frac{19}{10}a-\frac{19}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{9}{13})(\frac{-16}{19}-a)& =(\color{red}{b}+\color{orange}{\frac{9}{13}}).(\color{green}{-a}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{9}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{13})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{16}{19}b-\frac{9}{13}a-\frac{9}{13}.\frac{16}{19}& \text{Uitwerken } \\ & =-ab-\frac{16}{19}b-\frac{9}{13}a-\frac{144}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{12}{6}-q)(q+\frac{18}{18})& =(\color{red}{-q}+\color{orange}{2}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qq-1q+2q+2.1& \text{Uitwerken } \\ & =-q^2+((-1)+2)q+(-2) & \text{Neem samen} \\ &=-q^2+1q+(-2) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(x+\frac{-13}{18})(\frac{-7}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{-13}{18}}).(\color{green}{a}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{2}x-\frac{13}{18}a+\frac{13}{18}.\frac{7}{2}& \text{Uitwerken } \\ & =ax-\frac{7}{2}x-\frac{13}{18}a+\frac{91}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{13}{13})(p-\frac{-8}{12})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{2}{3}p+1p+1.\frac{2}{3}& \text{Uitwerken } \\ & =p^2+(\frac{2}{3}+1)p+\frac{2}{3} & \text{Neem samen} \\ &=p^2+\frac{5}{3}p+\frac{2}{3} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{10}{5}+x)(q-\frac{13}{16})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{16}x+2q-2.\frac{13}{16}& \text{Uitwerken } \\ & =qx-\frac{13}{16}x+2q-\frac{26}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{13}{16}x+2q-\frac{13}{8} & \text{Vereenvoudig} \\\end{align}\)