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

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Werk uit en vereenvoudig

1. \((a+\frac{-19}{11})(\frac{-2}{3}-b)\)
2. \((a+\frac{17}{3})(p-\frac{-2}{19})\)
3. \((14+b)(\frac{2}{4}+b)\)
4. \((x+\frac{-5}{6})(a-\frac{-7}{14})\)
5. \((\frac{6}{5}-x)(b+\frac{17}{12})\)
6. \((q+\frac{-1}{15})(a+\frac{-5}{15})\)
7. \((q+\frac{19}{11})(x-\frac{7}{8})\)
8. \((x-\frac{4}{9})(\frac{3}{3}+q)\)
9. \((\frac{-7}{5}-a)(\frac{10}{19}+q)\)
10. \((q+\frac{-16}{16})(a+\frac{8}{20})\)
11. \((\frac{11}{7}-q)(\frac{-13}{15}+x)\)
12. \((a-\frac{3}{17})(\frac{20}{5}+a)\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-19}{11})(\frac{-2}{3}-b)& =(\color{red}{a}+\color{orange}{\frac{-19}{11}}).(\color{green}{-b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{3}a+\frac{19}{11}b+\frac{19}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =-ab-\frac{2}{3}a+\frac{19}{11}b+\frac{38}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{17}{3})(p-\frac{-2}{19})& =(\color{red}{a}+\color{orange}{\frac{17}{3}}).(\color{green}{p}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{17}{3})} . \color{green}{(p)} + \color{orange}{(\frac{17}{3})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{19}a+\frac{17}{3}p+\frac{17}{3}.\frac{2}{19}& \text{Uitwerken } \\ & =ap+\frac{2}{19}a+\frac{17}{3}p+\frac{34}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(14+b)(\frac{2}{4}+b)& =(\color{red}{b}+\color{orange}{14}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(14)} . \color{green}{(b)} + \color{orange}{(14)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{2}b+14b+14.\frac{1}{2}& \text{Uitwerken } \\ & =b^2+(\frac{1}{2}+14)b+\frac{14}{2} & \text{Neem samen} \\ &=b^2+\frac{29}{2}b+\frac{14}{2} & \text{Maak de som} \\ &=b^2+\frac{29}{2}b+7 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(x+\frac{-5}{6})(a-\frac{-7}{14})& =(\color{red}{x}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}x-\frac{5}{6}a-\frac{5}{6}.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}x-\frac{5}{6}a-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{6}{5}-x)(b+\frac{17}{12})& =(\color{red}{-x}+\color{orange}{\frac{6}{5}}).(\color{green}{b}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{17}{12}x+\frac{6}{5}b+\frac{6}{5}.\frac{17}{12}& \text{Uitwerken } \\ & =-bx-\frac{17}{12}x+\frac{6}{5}b+\frac{102}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{17}{12}x+\frac{6}{5}b+\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(q+\frac{-1}{15})(a+\frac{-5}{15})& =(\color{red}{q}+\color{orange}{\frac{-1}{15}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{3}q-\frac{1}{15}a+\frac{1}{15}.\frac{1}{3}& \text{Uitwerken } \\ & =aq-\frac{1}{3}q-\frac{1}{15}a+\frac{1}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{19}{11})(x-\frac{7}{8})& =(\color{red}{q}+\color{orange}{\frac{19}{11}}).(\color{green}{x}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{19}{11})} . \color{green}{(x)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{8}q+\frac{19}{11}x-\frac{19}{11}.\frac{7}{8}& \text{Uitwerken } \\ & =qx-\frac{7}{8}q+\frac{19}{11}x-\frac{133}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x-\frac{4}{9})(\frac{3}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{-4}{9}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx+1x-\frac{4}{9}q-\frac{4}{9}.1& \text{Uitwerken } \\ & =qx+1x-\frac{4}{9}q-\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-7}{5}-a)(\frac{10}{19}+q)& =(\color{red}{-a}+\color{orange}{\frac{-7}{5}}).(\color{green}{q}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{10}{19}a-\frac{7}{5}q-\frac{7}{5}.\frac{10}{19}& \text{Uitwerken } \\ & =-aq-\frac{10}{19}a-\frac{7}{5}q-\frac{70}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{10}{19}a-\frac{7}{5}q-\frac{14}{19} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q+\frac{-16}{16})(a+\frac{8}{20})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{5}q-1a-1.\frac{2}{5}& \text{Uitwerken } \\ & =aq+\frac{2}{5}q-1a-\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{11}{7}-q)(\frac{-13}{15}+x)& =(\color{red}{-q}+\color{orange}{\frac{11}{7}}).(\color{green}{x}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{11}{7})} . \color{green}{(x)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{15}q+\frac{11}{7}x-\frac{11}{7}.\frac{13}{15}& \text{Uitwerken } \\ & =-qx+\frac{13}{15}q+\frac{11}{7}x-\frac{143}{105} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a-\frac{3}{17})(\frac{20}{5}+a)& =(\color{red}{a}+\color{orange}{\frac{-3}{17}}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{-3}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = aa+4a-\frac{3}{17}a-\frac{3}{17}.4& \text{Uitwerken } \\ & =a^2+(4+(\frac{-3}{17}))a-(\frac{-12}{17}) & \text{Neem samen} \\ &=a^2+\frac{65}{17}a-(\frac{-12}{17}) & \text{Maak de som} \\\end{align}\)