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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-20}{11}+a)(\frac{4}{4}-a)& =(\color{red}{a}+\color{orange}{\frac{-20}{11}}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-20}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aa+1a+\frac{20}{11}a-\frac{20}{11}.1& \text{Uitwerken } \\ & =-a^2+(1+\frac{20}{11})a-\frac{20}{11} & \text{Neem samen} \\ &=-a^2+\frac{31}{11}a-\frac{20}{11} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(p+\frac{17}{4})(q+\frac{6}{13})& =(\color{red}{p}+\color{orange}{\frac{17}{4}}).(\color{green}{q}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{17}{4})} . \color{green}{(q)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{6}{13}p+\frac{17}{4}q+\frac{17}{4}.\frac{6}{13}& \text{Uitwerken } \\ & =pq+\frac{6}{13}p+\frac{17}{4}q+\frac{102}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{6}{13}p+\frac{17}{4}q+\frac{51}{26} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-6}{19}+a)(b-\frac{2}{18})& =(\color{red}{a}+\color{orange}{\frac{-6}{19}}).(\color{green}{b}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-6}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{9}a-\frac{6}{19}b+\frac{6}{19}.\frac{1}{9}& \text{Uitwerken } \\ & =ab-\frac{1}{9}a-\frac{6}{19}b+\frac{6}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{9}a-\frac{6}{19}b+\frac{2}{57} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{3}{18}+a)(p+\frac{-15}{13})& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{p}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{1}{6})} . \color{green}{(p)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{13}a+\frac{1}{6}p-\frac{1}{6}.\frac{15}{13}& \text{Uitwerken } \\ & =ap-\frac{15}{13}a+\frac{1}{6}p-\frac{15}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{15}{13}a+\frac{1}{6}p-\frac{5}{26} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x+\frac{14}{13})(\frac{3}{3}+b)& =(\color{red}{x}+\color{orange}{\frac{14}{13}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{14}{13})} . \color{green}{(b)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x+\frac{14}{13}b+\frac{14}{13}.1& \text{Uitwerken } \\ & =bx+1x+\frac{14}{13}b+\frac{14}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-20}{17}+q)((-15)+x)& =(\color{red}{q}+\color{orange}{\frac{-20}{17}}).(\color{green}{x}+\color{blue}{(-15)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-15)} + \color{orange}{(\frac{-20}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = qx-15q-\frac{20}{17}x+\frac{20}{17}.15& \text{Uitwerken } \\ & =qx-15q-\frac{20}{17}x+\frac{300}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p-\frac{-4}{15})(\frac{12}{4}+a)& =(\color{red}{p}+\color{orange}{\frac{4}{15}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{4}{15})} . \color{green}{(a)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ap+3p+\frac{4}{15}a+\frac{4}{15}.3& \text{Uitwerken } \\ & =ap+3p+\frac{4}{15}a+\frac{12}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+3p+\frac{4}{15}a+\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{19}{10}+q)(p+\frac{-1}{17})& =(\color{red}{q}+\color{orange}{\frac{19}{10}}).(\color{green}{p}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{19}{10})} . \color{green}{(p)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{17}q+\frac{19}{10}p-\frac{19}{10}.\frac{1}{17}& \text{Uitwerken } \\ & =pq-\frac{1}{17}q+\frac{19}{10}p-\frac{19}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-18}{3}+a)(\frac{18}{7}+a)& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{a}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(-6)} . \color{green}{(a)} + \color{orange}{(-6)} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{18}{7}a-6a-6.\frac{18}{7}& \text{Uitwerken } \\ & =a^2+(\frac{18}{7}+(-6))a-(\frac{-108}{7}) & \text{Neem samen} \\ &=a^2-\frac{24}{7}a-(\frac{-108}{7}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(q-\frac{1}{9})(\frac{1}{6}-p)& =(\color{red}{q}+\color{orange}{\frac{-1}{9}}).(\color{green}{-p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{6}q+\frac{1}{9}p-\frac{1}{9}.\frac{1}{6}& \text{Uitwerken } \\ & =-pq+\frac{1}{6}q+\frac{1}{9}p-\frac{1}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{-13}{6})(p+\frac{-19}{10})& =(\color{red}{b}+\color{orange}{\frac{13}{6}}).(\color{green}{p}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{13}{6})} . \color{green}{(p)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{10}b+\frac{13}{6}p-\frac{13}{6}.\frac{19}{10}& \text{Uitwerken } \\ & =bp-\frac{19}{10}b+\frac{13}{6}p-\frac{247}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-6}{18}+x)(x+18)& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{x}+\color{blue}{18})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(18)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = xx+18x-\frac{1}{3}x-\frac{1}{3}.18& \text{Uitwerken } \\ & =x^2+(18+(\frac{-1}{3}))x-(\frac{-18}{3}) & \text{Neem samen} \\ &=x^2+\frac{53}{3}x-(\frac{-18}{3}) & \text{Maak de som} \\ &=x^2+\frac{53}{3}x+6 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)