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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{-11}{20})(x-\frac{-10}{11})& =(\color{red}{x}+\color{orange}{\frac{-11}{20}}).(\color{green}{x}+\color{blue}{\frac{10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{10}{11})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{10}{11})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{10}{11}x-\frac{11}{20}x-\frac{11}{20}.\frac{10}{11}& \text{Uitwerken } \\ & =x^2+(\frac{10}{11}+(\frac{-11}{20}))x-(\frac{-110}{220}) & \text{Neem samen} \\ &=x^2+\frac{79}{220}x-(\frac{-110}{220}) & \text{Maak de som} \\ &=x^2+\frac{79}{220}x+\frac{1}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
2. \(\begin{align}(b+\frac{-2}{3})(\frac{14}{3}+b)& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{14}{3}b-\frac{2}{3}b-\frac{2}{3}.\frac{14}{3}& \text{Uitwerken } \\ & =b^2+(\frac{14}{3}+(\frac{-2}{3}))b-(\frac{-28}{9}) & \text{Neem samen} \\ &=b^2+\frac{12}{3}b-(\frac{-28}{9}) & \text{Maak de som} \\ &=b^2+4b+\frac{28}{9} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
3. \(\begin{align}(\frac{-2}{20}+q)(\frac{19}{5}+p)& =(\color{red}{q}+\color{orange}{\frac{-1}{10}}).(\color{green}{p}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{19}{5}q-\frac{1}{10}p-\frac{1}{10}.\frac{19}{5}& \text{Uitwerken } \\ & =pq+\frac{19}{5}q-\frac{1}{10}p-\frac{19}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-6}{10}-x)(\frac{-16}{2}-x)& =(\color{red}{-x}+\color{orange}{\frac{-3}{5}}).(\color{green}{-x}+\color{blue}{(-8)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(-8)} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = xx+8x+\frac{3}{5}x+\frac{3}{5}.8& \text{Uitwerken } \\ & =x^2+(8+\frac{3}{5})x+\frac{24}{5} & \text{Neem samen} \\ &=x^2+\frac{43}{5}x+\frac{24}{5} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(q+1)(\frac{6}{20}+p)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{10}q+1p+1.\frac{3}{10}& \text{Uitwerken } \\ & =pq+\frac{3}{10}q+1p+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-10}{2}+x)(q-\frac{-11}{18})& =(\color{red}{x}+\color{orange}{(-5)}).(\color{green}{q}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(-5)} . \color{green}{(q)} + \color{orange}{(-5)} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{18}x-5q-5.\frac{11}{18}& \text{Uitwerken } \\ & =qx+\frac{11}{18}x-5q-\frac{55}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b-\frac{-15}{11})(p+\frac{-6}{18})& =(\color{red}{b}+\color{orange}{\frac{15}{11}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{15}{11})} . \color{green}{(p)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{3}b+\frac{15}{11}p-\frac{15}{11}.\frac{1}{3}& \text{Uitwerken } \\ & =bp-\frac{1}{3}b+\frac{15}{11}p-\frac{15}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{1}{3}b+\frac{15}{11}p-\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(p+\frac{3}{20})(\frac{16}{13}-b)& =(\color{red}{p}+\color{orange}{\frac{3}{20}}).(\color{green}{-b}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(\frac{3}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{16}{13}p-\frac{3}{20}b+\frac{3}{20}.\frac{16}{13}& \text{Uitwerken } \\ & =-bp+\frac{16}{13}p-\frac{3}{20}b+\frac{48}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{16}{13}p-\frac{3}{20}b+\frac{12}{65} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x+\frac{-12}{13})(\frac{-1}{13}-p)& =(\color{red}{x}+\color{orange}{\frac{-12}{13}}).(\color{green}{-p}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{13}x+\frac{12}{13}p+\frac{12}{13}.\frac{1}{13}& \text{Uitwerken } \\ & =-px-\frac{1}{13}x+\frac{12}{13}p+\frac{12}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-12}{2}+b)(p+\frac{-6}{3})& =(\color{red}{b}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bp-2b-6p+6.2& \text{Uitwerken } \\ & =bp-2b-6p+12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{19}{7})(\frac{-17}{5}-b)& =(\color{red}{b}+\color{orange}{\frac{-19}{7}}).(\color{green}{-b}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{17}{5}b+\frac{19}{7}b+\frac{19}{7}.\frac{17}{5}& \text{Uitwerken } \\ & =-b^2+((\frac{-17}{5})+\frac{19}{7})b+(\frac{-323}{35}) & \text{Neem samen} \\ &=-b^2-\frac{24}{35}b+(\frac{-323}{35}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(q+\frac{-1}{4})(\frac{-3}{16}-a)& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{-a}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{16}q+\frac{1}{4}a+\frac{1}{4}.\frac{3}{16}& \text{Uitwerken } \\ & =-aq-\frac{3}{16}q+\frac{1}{4}a+\frac{3}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)