Werk uit en vereenvoudig
- \((a+\frac{-20}{5})(x+\frac{12}{4})\)
- \((\frac{6}{3}+x)(\frac{16}{16}-q)\)
- \((q+\frac{-10}{9})(x+\frac{6}{11})\)
- \((x-\frac{-17}{8})(\frac{-8}{20}+b)\)
- \((b+\frac{-8}{8})(\frac{9}{13}+p)\)
- \((a+\frac{-6}{19})(a-\frac{1}{16})\)
- \((p+\frac{14}{8})(q+\frac{16}{9})\)
- \((\frac{-20}{14}-x)(b-\frac{20}{19})\)
- \((a+\frac{12}{11})(a-\frac{4}{5})\)
- \((x+\frac{-7}{11})(a+\frac{9}{19})\)
- \((x+\frac{-2}{5})(\frac{-6}{18}+p)\)
- \((q-\frac{-19}{14})(\frac{-18}{12}-a)\)
Werk uit en vereenvoudig
Verbetersleutel
- \(\begin{align}(a+\frac{-20}{5})(x+\frac{12}{4})& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(3)}
+ \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ax+3a-4x-4.3& \text{Uitwerken } \\ & =ax+3a-4x-12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(\frac{6}{3}+x)(\frac{16}{16}-q)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(1)}
+ \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1x-2q+2.1& \text{Uitwerken } \\ & =-qx+1x-2q+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(q+\frac{-10}{9})(x+\frac{6}{11})& =(\color{red}{q}+\color{orange}{\frac{-10}{9}}).(\color{green}{x}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{6}{11})}
+ \color{orange}{(\frac{-10}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{6}{11}q-\frac{10}{9}x-\frac{10}{9}.\frac{6}{11}& \text{Uitwerken } \\ & =qx+\frac{6}{11}q-\frac{10}{9}x-\frac{60}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{6}{11}q-\frac{10}{9}x-\frac{20}{33} & \text{Vereenvoudig} \\\end{align}\)
- \(\begin{align}(x-\frac{-17}{8})(\frac{-8}{20}+b)& =(\color{red}{x}+\color{orange}{\frac{17}{8}}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})}
+ \color{orange}{(\frac{17}{8})} . \color{green}{(b)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{5}x+\frac{17}{8}b-\frac{17}{8}.\frac{2}{5}& \text{Uitwerken } \\ & =bx-\frac{2}{5}x+\frac{17}{8}b-\frac{34}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{2}{5}x+\frac{17}{8}b-\frac{17}{20} & \text{Vereenvoudig} \\\end{align}\)
- \(\begin{align}(b+\frac{-8}{8})(\frac{9}{13}+p)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{9}{13})}
+ \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{13}b-1p-1.\frac{9}{13}& \text{Uitwerken } \\ & =bp+\frac{9}{13}b-1p-\frac{9}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(a+\frac{-6}{19})(a-\frac{1}{16})& =(\color{red}{a}+\color{orange}{\frac{-6}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{16})}
+ \color{orange}{(\frac{-6}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{16}a-\frac{6}{19}a+\frac{6}{19}.\frac{1}{16}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{16})+(\frac{-6}{19}))a+\frac{6}{304} & \text{Neem samen} \\ &=a^2-\frac{115}{304}a+\frac{6}{304} & \text{Maak de som} \\ &=a^2-\frac{115}{304}a+\frac{3}{152} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
- \(\begin{align}(p+\frac{14}{8})(q+\frac{16}{9})& =(\color{red}{p}+\color{orange}{\frac{7}{4}}).(\color{green}{q}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{16}{9})}
+ \color{orange}{(\frac{7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{16}{9}p+\frac{7}{4}q+\frac{7}{4}.\frac{16}{9}& \text{Uitwerken } \\ & =pq+\frac{16}{9}p+\frac{7}{4}q+\frac{112}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{16}{9}p+\frac{7}{4}q+\frac{28}{9} & \text{Vereenvoudig} \\\end{align}\)
- \(\begin{align}(\frac{-20}{14}-x)(b-\frac{20}{19})& =(\color{red}{-x}+\color{orange}{\frac{-10}{7}}).(\color{green}{b}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-20}{19})}
+ \color{orange}{(\frac{-10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{20}{19}x-\frac{10}{7}b+\frac{10}{7}.\frac{20}{19}& \text{Uitwerken } \\ & =-bx+\frac{20}{19}x-\frac{10}{7}b+\frac{200}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(a+\frac{12}{11})(a-\frac{4}{5})& =(\color{red}{a}+\color{orange}{\frac{12}{11}}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{5})}
+ \color{orange}{(\frac{12}{11})} . \color{green}{(a)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{4}{5}a+\frac{12}{11}a-\frac{12}{11}.\frac{4}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-4}{5})+\frac{12}{11})a-(\frac{-48}{55}) & \text{Neem samen} \\ &=a^2+\frac{16}{55}a-(\frac{-48}{55}) & \text{Maak de som} \\\end{align}\)
- \(\begin{align}(x+\frac{-7}{11})(a+\frac{9}{19})& =(\color{red}{x}+\color{orange}{\frac{-7}{11}}).(\color{green}{a}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{9}{19})}
+ \color{orange}{(\frac{-7}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{19}x-\frac{7}{11}a-\frac{7}{11}.\frac{9}{19}& \text{Uitwerken } \\ & =ax+\frac{9}{19}x-\frac{7}{11}a-\frac{63}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(x+\frac{-2}{5})(\frac{-6}{18}+p)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})}
+ \color{orange}{(\frac{-2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{3}x-\frac{2}{5}p+\frac{2}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =px-\frac{1}{3}x-\frac{2}{5}p+\frac{2}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(q-\frac{-19}{14})(\frac{-18}{12}-a)& =(\color{red}{q}+\color{orange}{\frac{19}{14}}).(\color{green}{-a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})}
+ \color{orange}{(\frac{19}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{2}q-\frac{19}{14}a-\frac{19}{14}.\frac{3}{2}& \text{Uitwerken } \\ & =-aq-\frac{3}{2}q-\frac{19}{14}a-\frac{57}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)