Werk uit en vereenvoudig
- \((p+10)(\frac{-11}{10}-q)\)
- \((x-\frac{-2}{19})(x+\frac{14}{9})\)
- \((q+\frac{5}{18})(q-\frac{-11}{3})\)
- \((x-\frac{-16}{7})(a-\frac{17}{15})\)
- \((\frac{13}{11}+a)(a+\frac{8}{15})\)
- \((\frac{16}{10}+p)(x+\frac{20}{19})\)
- \((b-\frac{6}{6})(x+\frac{6}{18})\)
- \((b+\frac{-7}{17})(q-\frac{-19}{10})\)
- \(((-7)+x)(a+\frac{-12}{20})\)
- \((\frac{3}{12}-x)(a+\frac{-5}{13})\)
- \((a+\frac{-6}{6})(q-\frac{-3}{11})\)
- \((p-\frac{-11}{20})(p+\frac{-7}{11})\)
Werk uit en vereenvoudig
Verbetersleutel
- \(\begin{align}(p+10)(\frac{-11}{10}-q)& =(\color{red}{p}+\color{orange}{10}).(\color{green}{-q}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{10})}
+ \color{orange}{(10)} . \color{green}{(-q)} + \color{orange}{(10)} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{11}{10}p-10q-10.\frac{11}{10}& \text{Uitwerken } \\ & =-pq-\frac{11}{10}p-10q-\frac{110}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{11}{10}p-10q-11 & \text{Vereenvoudig} \\\end{align}\)
- \(\begin{align}(x-\frac{-2}{19})(x+\frac{14}{9})& =(\color{red}{x}+\color{orange}{\frac{2}{19}}).(\color{green}{x}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{14}{9})}
+ \color{orange}{(\frac{2}{19})} . \color{green}{(x)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{14}{9}x+\frac{2}{19}x+\frac{2}{19}.\frac{14}{9}& \text{Uitwerken } \\ & =x^2+(\frac{14}{9}+\frac{2}{19})x+\frac{28}{171} & \text{Neem samen} \\ &=x^2+\frac{284}{171}x+\frac{28}{171} & \text{Maak de som} \\\end{align}\)
- \(\begin{align}(q+\frac{5}{18})(q-\frac{-11}{3})& =(\color{red}{q}+\color{orange}{\frac{5}{18}}).(\color{green}{q}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{11}{3})}
+ \color{orange}{(\frac{5}{18})} . \color{green}{(q)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{11}{3}q+\frac{5}{18}q+\frac{5}{18}.\frac{11}{3}& \text{Uitwerken } \\ & =q^2+(\frac{11}{3}+\frac{5}{18})q+\frac{55}{54} & \text{Neem samen} \\ &=q^2+\frac{71}{18}q+\frac{55}{54} & \text{Maak de som} \\\end{align}\)
- \(\begin{align}(x-\frac{-16}{7})(a-\frac{17}{15})& =(\color{red}{x}+\color{orange}{\frac{16}{7}}).(\color{green}{a}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{15})}
+ \color{orange}{(\frac{16}{7})} . \color{green}{(a)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{15}x+\frac{16}{7}a-\frac{16}{7}.\frac{17}{15}& \text{Uitwerken } \\ & =ax-\frac{17}{15}x+\frac{16}{7}a-\frac{272}{105} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(\frac{13}{11}+a)(a+\frac{8}{15})& =(\color{red}{a}+\color{orange}{\frac{13}{11}}).(\color{green}{a}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{8}{15})}
+ \color{orange}{(\frac{13}{11})} . \color{green}{(a)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{8}{15}a+\frac{13}{11}a+\frac{13}{11}.\frac{8}{15}& \text{Uitwerken } \\ & =a^2+(\frac{8}{15}+\frac{13}{11})a+\frac{104}{165} & \text{Neem samen} \\ &=a^2+\frac{283}{165}a+\frac{104}{165} & \text{Maak de som} \\\end{align}\)
- \(\begin{align}(\frac{16}{10}+p)(x+\frac{20}{19})& =(\color{red}{p}+\color{orange}{\frac{8}{5}}).(\color{green}{x}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{20}{19})}
+ \color{orange}{(\frac{8}{5})} . \color{green}{(x)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{20}{19}p+\frac{8}{5}x+\frac{8}{5}.\frac{20}{19}& \text{Uitwerken } \\ & =px+\frac{20}{19}p+\frac{8}{5}x+\frac{160}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{20}{19}p+\frac{8}{5}x+\frac{32}{19} & \text{Vereenvoudig} \\\end{align}\)
- \(\begin{align}(b-\frac{6}{6})(x+\frac{6}{18})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})}
+ \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{3}b-1x-1.\frac{1}{3}& \text{Uitwerken } \\ & =bx+\frac{1}{3}b-1x-\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(b+\frac{-7}{17})(q-\frac{-19}{10})& =(\color{red}{b}+\color{orange}{\frac{-7}{17}}).(\color{green}{q}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{19}{10})}
+ \color{orange}{(\frac{-7}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{10}b-\frac{7}{17}q-\frac{7}{17}.\frac{19}{10}& \text{Uitwerken } \\ & =bq+\frac{19}{10}b-\frac{7}{17}q-\frac{133}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}((-7)+x)(a+\frac{-12}{20})& =(\color{red}{x}+\color{orange}{(-7)}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{5})}
+ \color{orange}{(-7)} . \color{green}{(a)} + \color{orange}{(-7)} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{5}x-7a+7.\frac{3}{5}& \text{Uitwerken } \\ & =ax-\frac{3}{5}x-7a+\frac{21}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(\frac{3}{12}-x)(a+\frac{-5}{13})& =(\color{red}{-x}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{13})}
+ \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{13}x+\frac{1}{4}a-\frac{1}{4}.\frac{5}{13}& \text{Uitwerken } \\ & =-ax+\frac{5}{13}x+\frac{1}{4}a-\frac{5}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(a+\frac{-6}{6})(q-\frac{-3}{11})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{11})}
+ \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{11}a-1q-1.\frac{3}{11}& \text{Uitwerken } \\ & =aq+\frac{3}{11}a-1q-\frac{3}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(p-\frac{-11}{20})(p+\frac{-7}{11})& =(\color{red}{p}+\color{orange}{\frac{11}{20}}).(\color{green}{p}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{11})}
+ \color{orange}{(\frac{11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{7}{11}p+\frac{11}{20}p-\frac{11}{20}.\frac{7}{11}& \text{Uitwerken } \\ & =p^2+((\frac{-7}{11})+\frac{11}{20})p-(\frac{-77}{220}) & \text{Neem samen} \\ &=p^2-\frac{19}{220}p-(\frac{-77}{220}) & \text{Maak de som} \\ &=p^2-\frac{19}{220}p+\frac{7}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)