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

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Werk uit en vereenvoudig

1. \((\frac{-3}{6}+q)(\frac{-13}{19}+b)\)
2. \((p-\frac{-7}{9})(\frac{2}{14}-b)\)
3. \((q-\frac{12}{15})((-7)+x)\)
4. \((\frac{2}{11}+b)(q+\frac{-15}{13})\)
5. \((\frac{11}{13}+x)(\frac{-10}{14}-a)\)
6. \((x+\frac{-18}{12})(a-\frac{-8}{4})\)
7. \((\frac{-17}{13}+q)(\frac{-1}{17}-q)\)
8. \((\frac{18}{13}+p)(p+\frac{4}{7})\)
9. \((\frac{18}{2}+q)(\frac{10}{5}-x)\)
10. \((q-\frac{-19}{5})(\frac{8}{6}+a)\)
11. \((\frac{20}{5}-x)(\frac{-6}{12}-q)\)
12. \((p-\frac{13}{20})(\frac{-17}{6}+a)\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-3}{6}+q)(\frac{-13}{19}+b)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{19}q-\frac{1}{2}b+\frac{1}{2}.\frac{13}{19}& \text{Uitwerken } \\ & =bq-\frac{13}{19}q-\frac{1}{2}b+\frac{13}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{-7}{9})(\frac{2}{14}-b)& =(\color{red}{p}+\color{orange}{\frac{7}{9}}).(\color{green}{-b}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{7}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{7}p-\frac{7}{9}b+\frac{7}{9}.\frac{1}{7}& \text{Uitwerken } \\ & =-bp+\frac{1}{7}p-\frac{7}{9}b+\frac{7}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{7}p-\frac{7}{9}b+\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q-\frac{12}{15})((-7)+x)& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-7)} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = qx-7q-\frac{4}{5}x+\frac{4}{5}.7& \text{Uitwerken } \\ & =qx-7q-\frac{4}{5}x+\frac{28}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{2}{11}+b)(q+\frac{-15}{13})& =(\color{red}{b}+\color{orange}{\frac{2}{11}}).(\color{green}{q}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{2}{11})} . \color{green}{(q)} + \color{orange}{(\frac{2}{11})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{13}b+\frac{2}{11}q-\frac{2}{11}.\frac{15}{13}& \text{Uitwerken } \\ & =bq-\frac{15}{13}b+\frac{2}{11}q-\frac{30}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{11}{13}+x)(\frac{-10}{14}-a)& =(\color{red}{x}+\color{orange}{\frac{11}{13}}).(\color{green}{-a}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{11}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{7}x-\frac{11}{13}a-\frac{11}{13}.\frac{5}{7}& \text{Uitwerken } \\ & =-ax-\frac{5}{7}x-\frac{11}{13}a-\frac{55}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-18}{12})(a-\frac{-8}{4})& =(\color{red}{x}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2x-\frac{3}{2}a-\frac{3}{2}.2& \text{Uitwerken } \\ & =ax+2x-\frac{3}{2}a-\frac{6}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+2x-\frac{3}{2}a-3 & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-17}{13}+q)(\frac{-1}{17}-q)& =(\color{red}{q}+\color{orange}{\frac{-17}{13}}).(\color{green}{-q}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{-17}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{17}q+\frac{17}{13}q+\frac{17}{13}.\frac{1}{17}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{17})+\frac{17}{13})q+(\frac{-17}{221}) & \text{Neem samen} \\ &=-q^2+\frac{276}{221}q+(\frac{-17}{221}) & \text{Maak de som} \\ &=-q^2+\frac{276}{221}q+(\frac{-1}{13}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(\frac{18}{13}+p)(p+\frac{4}{7})& =(\color{red}{p}+\color{orange}{\frac{18}{13}}).(\color{green}{p}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{18}{13})} . \color{green}{(p)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{4}{7}p+\frac{18}{13}p+\frac{18}{13}.\frac{4}{7}& \text{Uitwerken } \\ & =p^2+(\frac{4}{7}+\frac{18}{13})p+\frac{72}{91} & \text{Neem samen} \\ &=p^2+\frac{178}{91}p+\frac{72}{91} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{18}{2}+q)(\frac{10}{5}-x)& =(\color{red}{q}+\color{orange}{9}).(\color{green}{-x}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(9)} . \color{green}{(-x)} + \color{orange}{(9)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qx+2q-9x+9.2& \text{Uitwerken } \\ & =-qx+2q-9x+18 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{-19}{5})(\frac{8}{6}+a)& =(\color{red}{q}+\color{orange}{\frac{19}{5}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{19}{5})} . \color{green}{(a)} + \color{orange}{(\frac{19}{5})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{3}q+\frac{19}{5}a+\frac{19}{5}.\frac{4}{3}& \text{Uitwerken } \\ & =aq+\frac{4}{3}q+\frac{19}{5}a+\frac{76}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{20}{5}-x)(\frac{-6}{12}-q)& =(\color{red}{-x}+\color{orange}{4}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(4)} . \color{green}{(-q)} + \color{orange}{(4)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}x-4q-4.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}x-4q-\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{2}x-4q-2 & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(p-\frac{13}{20})(\frac{-17}{6}+a)& =(\color{red}{p}+\color{orange}{\frac{-13}{20}}).(\color{green}{a}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{17}{6}p-\frac{13}{20}a+\frac{13}{20}.\frac{17}{6}& \text{Uitwerken } \\ & =ap-\frac{17}{6}p-\frac{13}{20}a+\frac{221}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)