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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{-11}{17})(q-\frac{-4}{13})& =(\color{red}{x}+\color{orange}{\frac{-11}{17}}).(\color{green}{q}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{-11}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{13}x-\frac{11}{17}q-\frac{11}{17}.\frac{4}{13}& \text{Uitwerken } \\ & =qx+\frac{4}{13}x-\frac{11}{17}q-\frac{44}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{-14}{10})(\frac{-4}{9}-b)& =(\color{red}{x}+\color{orange}{\frac{-7}{5}}).(\color{green}{-b}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{9}x+\frac{7}{5}b+\frac{7}{5}.\frac{4}{9}& \text{Uitwerken } \\ & =-bx-\frac{4}{9}x+\frac{7}{5}b+\frac{28}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{-15}{2})(\frac{-11}{12}-q)& =(\color{red}{x}+\color{orange}{\frac{15}{2}}).(\color{green}{-q}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{15}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{11}{12}x-\frac{15}{2}q-\frac{15}{2}.\frac{11}{12}& \text{Uitwerken } \\ & =-qx-\frac{11}{12}x-\frac{15}{2}q-\frac{165}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{11}{12}x-\frac{15}{2}q-\frac{55}{8} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p-\frac{15}{11})(\frac{-3}{20}+x)& =(\color{red}{p}+\color{orange}{\frac{-15}{11}}).(\color{green}{x}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{20}p-\frac{15}{11}x+\frac{15}{11}.\frac{3}{20}& \text{Uitwerken } \\ & =px-\frac{3}{20}p-\frac{15}{11}x+\frac{45}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{3}{20}p-\frac{15}{11}x+\frac{9}{44} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p-\frac{-11}{17})(x+\frac{12}{17})& =(\color{red}{p}+\color{orange}{\frac{11}{17}}).(\color{green}{x}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{11}{17})} . \color{green}{(x)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{12}{17}p+\frac{11}{17}x+\frac{11}{17}.\frac{12}{17}& \text{Uitwerken } \\ & =px+\frac{12}{17}p+\frac{11}{17}x+\frac{132}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-5}{2})(a-\frac{-3}{3})& =(\color{red}{x}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1x-\frac{5}{2}a-\frac{5}{2}.1& \text{Uitwerken } \\ & =ax+1x-\frac{5}{2}a-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-1}{5}-a)(q+\frac{-7}{3})& =(\color{red}{-a}+\color{orange}{\frac{-1}{5}}).(\color{green}{q}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{3}a-\frac{1}{5}q+\frac{1}{5}.\frac{7}{3}& \text{Uitwerken } \\ & =-aq+\frac{7}{3}a-\frac{1}{5}q+\frac{7}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{-11}{6})((-13)-x)& =(\color{red}{p}+\color{orange}{\frac{-11}{6}}).(\color{green}{-x}+\color{blue}{(-13)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(-13)} + \color{orange}{(\frac{-11}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = -px-13p+\frac{11}{6}x+\frac{11}{6}.13& \text{Uitwerken } \\ & =-px-13p+\frac{11}{6}x+\frac{143}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{3}{6})(b-10)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{(-10)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-10)} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = bx-10x+\frac{1}{2}b-\frac{1}{2}.10& \text{Uitwerken } \\ & =bx-10x+\frac{1}{2}b-\frac{10}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-10x+\frac{1}{2}b-5 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(b+\frac{4}{7})(\frac{3}{11}-b)& =(\color{red}{b}+\color{orange}{\frac{4}{7}}).(\color{green}{-b}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(\frac{4}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{3}{11}b-\frac{4}{7}b+\frac{4}{7}.\frac{3}{11}& \text{Uitwerken } \\ & =-b^2+(\frac{3}{11}+(\frac{-4}{7}))b+(\frac{-12}{77}) & \text{Neem samen} \\ &=-b^2-\frac{23}{77}b+(\frac{-12}{77}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-16}{17}-p)(p+\frac{6}{17})& =(\color{red}{-p}+\color{orange}{\frac{-16}{17}}).(\color{green}{p}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{6}{17}p-\frac{16}{17}p-\frac{16}{17}.\frac{6}{17}& \text{Uitwerken } \\ & =-p^2+((\frac{-6}{17})+(\frac{-16}{17}))p-\frac{96}{289} & \text{Neem samen} \\ &=-p^2-\frac{22}{17}p-\frac{96}{289} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-13}{11}-x)((-15)-q)& =(\color{red}{-x}+\color{orange}{\frac{-13}{11}}).(\color{green}{-q}+\color{blue}{(-15)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(-15)} + \color{orange}{(\frac{-13}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = qx+15x+\frac{13}{11}q+\frac{13}{11}.15& \text{Uitwerken } \\ & =qx+15x+\frac{13}{11}q+\frac{195}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)