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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(17+q)(q-\frac{-18}{15})& =(\color{red}{q}+\color{orange}{17}).(\color{green}{q}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(17)} . \color{green}{(q)} + \color{orange}{(17)} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{6}{5}q+17q+17.\frac{6}{5}& \text{Uitwerken } \\ & =q^2+(\frac{6}{5}+17)q+\frac{102}{5} & \text{Neem samen} \\ &=q^2+\frac{91}{5}q+\frac{102}{5} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{-17}{3}-a)(\frac{-8}{13}-b)& =(\color{red}{-a}+\color{orange}{\frac{-17}{3}}).(\color{green}{-b}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{13}a+\frac{17}{3}b+\frac{17}{3}.\frac{8}{13}& \text{Uitwerken } \\ & =ab+\frac{8}{13}a+\frac{17}{3}b+\frac{136}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{17}{12}-x)(\frac{-9}{4}-b)& =(\color{red}{-x}+\color{orange}{\frac{17}{12}}).(\color{green}{-b}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{17}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{4}x-\frac{17}{12}b-\frac{17}{12}.\frac{9}{4}& \text{Uitwerken } \\ & =bx+\frac{9}{4}x-\frac{17}{12}b-\frac{153}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{9}{4}x-\frac{17}{12}b-\frac{51}{16} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(x-\frac{19}{14})(\frac{12}{13}+a)& =(\color{red}{x}+\color{orange}{\frac{-19}{14}}).(\color{green}{a}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{12}{13}x-\frac{19}{14}a-\frac{19}{14}.\frac{12}{13}& \text{Uitwerken } \\ & =ax+\frac{12}{13}x-\frac{19}{14}a-\frac{228}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{12}{13}x-\frac{19}{14}a-\frac{114}{91} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-16}{14}+a)(p-\frac{3}{3})& =(\color{red}{a}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a-\frac{8}{7}p+\frac{8}{7}.1& \text{Uitwerken } \\ & =ap-1a-\frac{8}{7}p+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-12}{12}+p)(\frac{20}{10}-b)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bp+2p+1b-1.2& \text{Uitwerken } \\ & =-bp+2p+1b-2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{3}{10}+p)(a+\frac{-17}{17})& =(\color{red}{p}+\color{orange}{\frac{3}{10}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1p+\frac{3}{10}a-\frac{3}{10}.1& \text{Uitwerken } \\ & =ap-1p+\frac{3}{10}a-\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{-17}{12})(\frac{-9}{6}-q)& =(\color{red}{p}+\color{orange}{\frac{-17}{12}}).(\color{green}{-q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{2}p+\frac{17}{12}q+\frac{17}{12}.\frac{3}{2}& \text{Uitwerken } \\ & =-pq-\frac{3}{2}p+\frac{17}{12}q+\frac{51}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{3}{2}p+\frac{17}{12}q+\frac{17}{8} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q-\frac{-1}{14})((-10)-b)& =(\color{red}{q}+\color{orange}{\frac{1}{14}}).(\color{green}{-b}+\color{blue}{(-10)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(-10)} + \color{orange}{(\frac{1}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -bq-10q-\frac{1}{14}b-\frac{1}{14}.10& \text{Uitwerken } \\ & =-bq-10q-\frac{1}{14}b-\frac{10}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-10q-\frac{1}{14}b-\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{18}{3}+p)(p+\frac{-6}{3})& =(\color{red}{p}+\color{orange}{6}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pp-2p+6p-6.2& \text{Uitwerken } \\ & =p^2+((-2)+6)p-(-12) & \text{Neem samen} \\ &=p^2+4p-(-12) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(x+\frac{-1}{17})(\frac{-1}{14}+b)& =(\color{red}{x}+\color{orange}{\frac{-1}{17}}).(\color{green}{b}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{14}x-\frac{1}{17}b+\frac{1}{17}.\frac{1}{14}& \text{Uitwerken } \\ & =bx-\frac{1}{14}x-\frac{1}{17}b+\frac{1}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{7}{8})(\frac{-20}{11}+q)& =(\color{red}{b}+\color{orange}{\frac{7}{8}}).(\color{green}{q}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{20}{11}b+\frac{7}{8}q-\frac{7}{8}.\frac{20}{11}& \text{Uitwerken } \\ & =bq-\frac{20}{11}b+\frac{7}{8}q-\frac{140}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{20}{11}b+\frac{7}{8}q-\frac{35}{22} & \text{Vereenvoudig} \\\end{align}\)