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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{19}{15})(\frac{17}{15}-a)& =(\color{red}{b}+\color{orange}{\frac{19}{15}}).(\color{green}{-a}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(\frac{19}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{17}{15}b-\frac{19}{15}a+\frac{19}{15}.\frac{17}{15}& \text{Uitwerken } \\ & =-ab+\frac{17}{15}b-\frac{19}{15}a+\frac{323}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{4}{14}+b)(p-9)& =(\color{red}{b}+\color{orange}{\frac{2}{7}}).(\color{green}{p}+\color{blue}{(-9)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-9)} + \color{orange}{(\frac{2}{7})} . \color{green}{(p)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = bp-9b+\frac{2}{7}p-\frac{2}{7}.9& \text{Uitwerken } \\ & =bp-9b+\frac{2}{7}p-\frac{18}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{1}{16})(p-14)& =(\color{red}{b}+\color{orange}{\frac{1}{16}}).(\color{green}{p}+\color{blue}{(-14)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-14)} + \color{orange}{(\frac{1}{16})} . \color{green}{(p)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = bp-14b+\frac{1}{16}p-\frac{1}{16}.14& \text{Uitwerken } \\ & =bp-14b+\frac{1}{16}p-\frac{14}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-14b+\frac{1}{16}p-\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(15+q)(a-\frac{18}{3})& =(\color{red}{q}+\color{orange}{15}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-6)} + \color{orange}{(15)} . \color{green}{(a)} + \color{orange}{(15)} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = aq-6q+15a-15.6& \text{Uitwerken } \\ & =aq-6q+15a-90 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{3}{3}+x)(q+\frac{-14}{20})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{10}x+1q-1.\frac{7}{10}& \text{Uitwerken } \\ & =qx-\frac{7}{10}x+1q-\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-9}{15}-b)(a-\frac{-1}{13})& =(\color{red}{-b}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{13}b-\frac{3}{5}a-\frac{3}{5}.\frac{1}{13}& \text{Uitwerken } \\ & =-ab-\frac{1}{13}b-\frac{3}{5}a-\frac{3}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-18}{8}+q)(\frac{9}{6}+p)& =(\color{red}{q}+\color{orange}{\frac{-9}{4}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{2}q-\frac{9}{4}p-\frac{9}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =pq+\frac{3}{2}q-\frac{9}{4}p-\frac{27}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q+\frac{3}{5})(b+\frac{-1}{12})& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{12}q+\frac{3}{5}b-\frac{3}{5}.\frac{1}{12}& \text{Uitwerken } \\ & =bq-\frac{1}{12}q+\frac{3}{5}b-\frac{3}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{12}q+\frac{3}{5}b-\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{9}{11}-a)(\frac{20}{10}-a)& =(\color{red}{-a}+\color{orange}{\frac{9}{11}}).(\color{green}{-a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(\frac{9}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aa-2a-\frac{9}{11}a+\frac{9}{11}.2& \text{Uitwerken } \\ & =a^2+((-2)+(\frac{-9}{11}))a+\frac{18}{11} & \text{Neem samen} \\ &=a^2-\frac{31}{11}a+\frac{18}{11} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{9}{8}-p)(p-\frac{-16}{14})& =(\color{red}{-p}+\color{orange}{\frac{9}{8}}).(\color{green}{p}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{9}{8})} . \color{green}{(p)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{8}{7}p+\frac{9}{8}p+\frac{9}{8}.\frac{8}{7}& \text{Uitwerken } \\ & =-p^2+((\frac{-8}{7})+\frac{9}{8})p+(\frac{-72}{56}) & \text{Neem samen} \\ &=-p^2-\frac{1}{56}p+(\frac{-72}{56}) & \text{Maak de som} \\ &=-p^2-\frac{1}{56}p+(\frac{-9}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(a+\frac{-17}{17})(\frac{-12}{20}+q)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{5}a-1q+1.\frac{3}{5}& \text{Uitwerken } \\ & =aq-\frac{3}{5}a-1q+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{6}{8}-a)(x+\frac{10}{13})& =(\color{red}{-a}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{10}{13}a+\frac{3}{4}x+\frac{3}{4}.\frac{10}{13}& \text{Uitwerken } \\ & =-ax-\frac{10}{13}a+\frac{3}{4}x+\frac{30}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{10}{13}a+\frac{3}{4}x+\frac{15}{26} & \text{Vereenvoudig} \\\end{align}\)