Werk uit en vereenvoudig
- \((\frac{16}{12}-q)(\frac{18}{14}+q)\)
- \((b-\frac{-20}{16})(\frac{-8}{15}-b)\)
- \((\frac{17}{5}+x)(a+\frac{-6}{18})\)
- \((\frac{20}{10}+a)(x-\frac{12}{7})\)
- \((p+\frac{13}{4})(q+\frac{17}{13})\)
- \((p-\frac{6}{10})(p-\frac{-12}{11})\)
- \((x+\frac{-5}{18})(a-\frac{-15}{5})\)
- \((\frac{-17}{17}-a)(x-\frac{2}{7})\)
- \((b+\frac{-10}{3})(\frac{-6}{11}-b)\)
- \((q-\frac{14}{13})(x-\frac{-9}{16})\)
- \((b+\frac{6}{2})(\frac{-20}{17}+x)\)
- \((p+\frac{1}{13})(\frac{1}{8}+b)\)
Werk uit en vereenvoudig
Verbetersleutel
- \(\begin{align}(\frac{16}{12}-q)(\frac{18}{14}+q)& =(\color{red}{-q}+\color{orange}{\frac{4}{3}}).(\color{green}{q}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{7})}
+ \color{orange}{(\frac{4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{9}{7}q+\frac{4}{3}q+\frac{4}{3}.\frac{9}{7}& \text{Uitwerken } \\ & =-q^2+((\frac{-9}{7})+\frac{4}{3})q+(\frac{-36}{21}) & \text{Neem samen} \\ &=-q^2+\frac{1}{21}q+(\frac{-36}{21}) & \text{Maak de som} \\ &=-q^2+\frac{1}{21}q+(\frac{-12}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
- \(\begin{align}(b-\frac{-20}{16})(\frac{-8}{15}-b)& =(\color{red}{b}+\color{orange}{\frac{5}{4}}).(\color{green}{-b}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{15})}
+ \color{orange}{(\frac{5}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{8}{15}b-\frac{5}{4}b-\frac{5}{4}.\frac{8}{15}& \text{Uitwerken } \\ & =-b^2+((\frac{-8}{15})+(\frac{-5}{4}))b-\frac{40}{60} & \text{Neem samen} \\ &=-b^2-\frac{107}{60}b-\frac{40}{60} & \text{Maak de som} \\ &=-b^2-\frac{107}{60}b-\frac{2}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
- \(\begin{align}(\frac{17}{5}+x)(a+\frac{-6}{18})& =(\color{red}{x}+\color{orange}{\frac{17}{5}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})}
+ \color{orange}{(\frac{17}{5})} . \color{green}{(a)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{3}x+\frac{17}{5}a-\frac{17}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =ax-\frac{1}{3}x+\frac{17}{5}a-\frac{17}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(\frac{20}{10}+a)(x-\frac{12}{7})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{7})}
+ \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{12}{7}a+2x-2.\frac{12}{7}& \text{Uitwerken } \\ & =ax-\frac{12}{7}a+2x-\frac{24}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(p+\frac{13}{4})(q+\frac{17}{13})& =(\color{red}{p}+\color{orange}{\frac{13}{4}}).(\color{green}{q}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{17}{13})}
+ \color{orange}{(\frac{13}{4})} . \color{green}{(q)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{17}{13}p+\frac{13}{4}q+\frac{13}{4}.\frac{17}{13}& \text{Uitwerken } \\ & =pq+\frac{17}{13}p+\frac{13}{4}q+\frac{221}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{17}{13}p+\frac{13}{4}q+\frac{17}{4} & \text{Vereenvoudig} \\\end{align}\)
- \(\begin{align}(p-\frac{6}{10})(p-\frac{-12}{11})& =(\color{red}{p}+\color{orange}{\frac{-3}{5}}).(\color{green}{p}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{12}{11})}
+ \color{orange}{(\frac{-3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{12}{11}p-\frac{3}{5}p-\frac{3}{5}.\frac{12}{11}& \text{Uitwerken } \\ & =p^2+(\frac{12}{11}+(\frac{-3}{5}))p-(\frac{-36}{55}) & \text{Neem samen} \\ &=p^2+\frac{27}{55}p-(\frac{-36}{55}) & \text{Maak de som} \\\end{align}\)
- \(\begin{align}(x+\frac{-5}{18})(a-\frac{-15}{5})& =(\color{red}{x}+\color{orange}{\frac{-5}{18}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(3)}
+ \color{orange}{(\frac{-5}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ax+3x-\frac{5}{18}a-\frac{5}{18}.3& \text{Uitwerken } \\ & =ax+3x-\frac{5}{18}a-\frac{15}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+3x-\frac{5}{18}a-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
- \(\begin{align}(\frac{-17}{17}-a)(x-\frac{2}{7})& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{7})}
+ \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{7}a-1x+1.\frac{2}{7}& \text{Uitwerken } \\ & =-ax+\frac{2}{7}a-1x+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(b+\frac{-10}{3})(\frac{-6}{11}-b)& =(\color{red}{b}+\color{orange}{\frac{-10}{3}}).(\color{green}{-b}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{11})}
+ \color{orange}{(\frac{-10}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{6}{11}b+\frac{10}{3}b+\frac{10}{3}.\frac{6}{11}& \text{Uitwerken } \\ & =-b^2+((\frac{-6}{11})+\frac{10}{3})b+(\frac{-60}{33}) & \text{Neem samen} \\ &=-b^2+\frac{92}{33}b+(\frac{-60}{33}) & \text{Maak de som} \\ &=-b^2+\frac{92}{33}b+(\frac{-20}{11}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
- \(\begin{align}(q-\frac{14}{13})(x-\frac{-9}{16})& =(\color{red}{q}+\color{orange}{\frac{-14}{13}}).(\color{green}{x}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{16})}
+ \color{orange}{(\frac{-14}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{16}q-\frac{14}{13}x-\frac{14}{13}.\frac{9}{16}& \text{Uitwerken } \\ & =qx+\frac{9}{16}q-\frac{14}{13}x-\frac{126}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{9}{16}q-\frac{14}{13}x-\frac{63}{104} & \text{Vereenvoudig} \\\end{align}\)
- \(\begin{align}(b+\frac{6}{2})(\frac{-20}{17}+x)& =(\color{red}{b}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{17})}
+ \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{20}{17}b+3x-3.\frac{20}{17}& \text{Uitwerken } \\ & =bx-\frac{20}{17}b+3x-\frac{60}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(p+\frac{1}{13})(\frac{1}{8}+b)& =(\color{red}{p}+\color{orange}{\frac{1}{13}}).(\color{green}{b}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{8})}
+ \color{orange}{(\frac{1}{13})} . \color{green}{(b)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{8}p+\frac{1}{13}b+\frac{1}{13}.\frac{1}{8}& \text{Uitwerken } \\ & =bp+\frac{1}{8}p+\frac{1}{13}b+\frac{1}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)