Werk uit en vereenvoudig
- \((b-\frac{1}{19})(\frac{-16}{15}-p)\)
- \((\frac{6}{2}-x)(\frac{-7}{7}-q)\)
- \((\frac{15}{4}+b)(a+(-19))\)
- \((q-\frac{-20}{2})(\frac{6}{6}-a)\)
- \((\frac{19}{9}+a)(x+\frac{6}{16})\)
- \((20+q)((-10)+p)\)
- \((\frac{17}{12}-x)(\frac{20}{16}-x)\)
- \((a+\frac{20}{6})(a+\frac{3}{6})\)
- \((\frac{-8}{17}-b)(a+\frac{3}{7})\)
- \((\frac{20}{8}+a)(\frac{-13}{7}+x)\)
- \((p+\frac{16}{13})((-19)-a)\)
- \((p-\frac{-19}{2})(\frac{-15}{3}-a)\)
Werk uit en vereenvoudig
Verbetersleutel
- \(\begin{align}(b-\frac{1}{19})(\frac{-16}{15}-p)& =(\color{red}{b}+\color{orange}{\frac{-1}{19}}).(\color{green}{-p}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{15})}
+ \color{orange}{(\frac{-1}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{16}{15}b+\frac{1}{19}p+\frac{1}{19}.\frac{16}{15}& \text{Uitwerken } \\ & =-bp-\frac{16}{15}b+\frac{1}{19}p+\frac{16}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(\frac{6}{2}-x)(\frac{-7}{7}-q)& =(\color{red}{-x}+\color{orange}{3}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(-1)}
+ \color{orange}{(3)} . \color{green}{(-q)} + \color{orange}{(3)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx+1x-3q-3.1& \text{Uitwerken } \\ & =qx+1x-3q-3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(\frac{15}{4}+b)(a+(-19))& =(\color{red}{b}+\color{orange}{\frac{15}{4}}).(\color{green}{a}+\color{blue}{(-19)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-19)}
+ \color{orange}{(\frac{15}{4})} . \color{green}{(a)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = ab-19b+\frac{15}{4}a-\frac{15}{4}.19& \text{Uitwerken } \\ & =ab-19b+\frac{15}{4}a-\frac{285}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(q-\frac{-20}{2})(\frac{6}{6}-a)& =(\color{red}{q}+\color{orange}{10}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(1)}
+ \color{orange}{(10)} . \color{green}{(-a)} + \color{orange}{(10)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1q-10a+10.1& \text{Uitwerken } \\ & =-aq+1q-10a+10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(\frac{19}{9}+a)(x+\frac{6}{16})& =(\color{red}{a}+\color{orange}{\frac{19}{9}}).(\color{green}{x}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{8})}
+ \color{orange}{(\frac{19}{9})} . \color{green}{(x)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{8}a+\frac{19}{9}x+\frac{19}{9}.\frac{3}{8}& \text{Uitwerken } \\ & =ax+\frac{3}{8}a+\frac{19}{9}x+\frac{57}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{8}a+\frac{19}{9}x+\frac{19}{24} & \text{Vereenvoudig} \\\end{align}\)
- \(\begin{align}(20+q)((-10)+p)& =(\color{red}{q}+\color{orange}{20}).(\color{green}{p}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-10)}
+ \color{orange}{(20)} . \color{green}{(p)} + \color{orange}{(20)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = pq-10q+20p-20.10& \text{Uitwerken } \\ & =pq-10q+20p-200 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(\frac{17}{12}-x)(\frac{20}{16}-x)& =(\color{red}{-x}+\color{orange}{\frac{17}{12}}).(\color{green}{-x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{4})}
+ \color{orange}{(\frac{17}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{5}{4}x-\frac{17}{12}x+\frac{17}{12}.\frac{5}{4}& \text{Uitwerken } \\ & =x^2+((\frac{-5}{4})+(\frac{-17}{12}))x+\frac{85}{48} & \text{Neem samen} \\ &=x^2-\frac{32}{12}x+\frac{85}{48} & \text{Maak de som} \\ &=x^2-\frac{8}{3}x+\frac{85}{48} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
- \(\begin{align}(a+\frac{20}{6})(a+\frac{3}{6})& =(\color{red}{a}+\color{orange}{\frac{10}{3}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})}
+ \color{orange}{(\frac{10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{2}a+\frac{10}{3}a+\frac{10}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =a^2+(\frac{1}{2}+\frac{10}{3})a+\frac{10}{6} & \text{Neem samen} \\ &=a^2+\frac{23}{6}a+\frac{10}{6} & \text{Maak de som} \\ &=a^2+\frac{23}{6}a+\frac{5}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
- \(\begin{align}(\frac{-8}{17}-b)(a+\frac{3}{7})& =(\color{red}{-b}+\color{orange}{\frac{-8}{17}}).(\color{green}{a}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{7})}
+ \color{orange}{(\frac{-8}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{7}b-\frac{8}{17}a-\frac{8}{17}.\frac{3}{7}& \text{Uitwerken } \\ & =-ab-\frac{3}{7}b-\frac{8}{17}a-\frac{24}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(\frac{20}{8}+a)(\frac{-13}{7}+x)& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{7})}
+ \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{7}a+\frac{5}{2}x-\frac{5}{2}.\frac{13}{7}& \text{Uitwerken } \\ & =ax-\frac{13}{7}a+\frac{5}{2}x-\frac{65}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(p+\frac{16}{13})((-19)-a)& =(\color{red}{p}+\color{orange}{\frac{16}{13}}).(\color{green}{-a}+\color{blue}{(-19)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(-19)}
+ \color{orange}{(\frac{16}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = -ap-19p-\frac{16}{13}a-\frac{16}{13}.19& \text{Uitwerken } \\ & =-ap-19p-\frac{16}{13}a-\frac{304}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
- \(\begin{align}(p-\frac{-19}{2})(\frac{-15}{3}-a)& =(\color{red}{p}+\color{orange}{\frac{19}{2}}).(\color{green}{-a}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(-5)}
+ \color{orange}{(\frac{19}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -ap-5p-\frac{19}{2}a-\frac{19}{2}.5& \text{Uitwerken } \\ & =-ap-5p-\frac{19}{2}a-\frac{95}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)