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

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Werk uit en vereenvoudig

1. \((\frac{-10}{11}-x)(\frac{-12}{6}+q)\)
2. \((x+\frac{-12}{9})(q+\frac{-7}{6})\)
3. \((\frac{14}{19}-b)(\frac{20}{16}+b)\)
4. \((a-\frac{12}{8})(\frac{-11}{20}-x)\)
5. \((\frac{-3}{7}-b)(\frac{20}{7}-x)\)
6. \((x+\frac{-18}{17})(\frac{-11}{6}-x)\)
7. \((b+\frac{12}{7})(\frac{-15}{9}-b)\)
8. \((x-\frac{20}{6})(\frac{17}{11}-q)\)
9. \((\frac{15}{20}+p)(a+\frac{-7}{2})\)
10. \((x+\frac{13}{15})(q-\frac{4}{20})\)
11. \((x+\frac{5}{18})(b+\frac{-11}{6})\)
12. \((\frac{-11}{9}-a)(p+\frac{11}{3})\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{11}-x)(\frac{-12}{6}+q)& =(\color{red}{-x}+\color{orange}{\frac{-10}{11}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-10}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -qx+2x-\frac{10}{11}q+\frac{10}{11}.2& \text{Uitwerken } \\ & =-qx+2x-\frac{10}{11}q+\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{-12}{9})(q+\frac{-7}{6})& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{6}x-\frac{4}{3}q+\frac{4}{3}.\frac{7}{6}& \text{Uitwerken } \\ & =qx-\frac{7}{6}x-\frac{4}{3}q+\frac{28}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{7}{6}x-\frac{4}{3}q+\frac{14}{9} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{14}{19}-b)(\frac{20}{16}+b)& =(\color{red}{-b}+\color{orange}{\frac{14}{19}}).(\color{green}{b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{14}{19})} . \color{green}{(b)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{5}{4}b+\frac{14}{19}b+\frac{14}{19}.\frac{5}{4}& \text{Uitwerken } \\ & =-b^2+((\frac{-5}{4})+\frac{14}{19})b+(\frac{-70}{76}) & \text{Neem samen} \\ &=-b^2-\frac{39}{76}b+(\frac{-70}{76}) & \text{Maak de som} \\ &=-b^2-\frac{39}{76}b+(\frac{-35}{38}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(a-\frac{12}{8})(\frac{-11}{20}-x)& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{20}a+\frac{3}{2}x+\frac{3}{2}.\frac{11}{20}& \text{Uitwerken } \\ & =-ax-\frac{11}{20}a+\frac{3}{2}x+\frac{33}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-3}{7}-b)(\frac{20}{7}-x)& =(\color{red}{-b}+\color{orange}{\frac{-3}{7}}).(\color{green}{-x}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{20}{7}b+\frac{3}{7}x-\frac{3}{7}.\frac{20}{7}& \text{Uitwerken } \\ & =bx-\frac{20}{7}b+\frac{3}{7}x-\frac{60}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-18}{17})(\frac{-11}{6}-x)& =(\color{red}{x}+\color{orange}{\frac{-18}{17}}).(\color{green}{-x}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{11}{6}x+\frac{18}{17}x+\frac{18}{17}.\frac{11}{6}& \text{Uitwerken } \\ & =-x^2+((\frac{-11}{6})+\frac{18}{17})x+(\frac{-198}{102}) & \text{Neem samen} \\ &=-x^2-\frac{79}{102}x+(\frac{-198}{102}) & \text{Maak de som} \\ &=-x^2-\frac{79}{102}x+(\frac{-33}{17}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(b+\frac{12}{7})(\frac{-15}{9}-b)& =(\color{red}{b}+\color{orange}{\frac{12}{7}}).(\color{green}{-b}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{12}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{12}{7})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{5}{3}b-\frac{12}{7}b-\frac{12}{7}.\frac{5}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-5}{3})+(\frac{-12}{7}))b-\frac{60}{21} & \text{Neem samen} \\ &=-b^2-\frac{71}{21}b-\frac{60}{21} & \text{Maak de som} \\ &=-b^2-\frac{71}{21}b-\frac{20}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(x-\frac{20}{6})(\frac{17}{11}-q)& =(\color{red}{x}+\color{orange}{\frac{-10}{3}}).(\color{green}{-q}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{17}{11}x+\frac{10}{3}q-\frac{10}{3}.\frac{17}{11}& \text{Uitwerken } \\ & =-qx+\frac{17}{11}x+\frac{10}{3}q-\frac{170}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{15}{20}+p)(a+\frac{-7}{2})& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{a}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{2}p+\frac{3}{4}a-\frac{3}{4}.\frac{7}{2}& \text{Uitwerken } \\ & =ap-\frac{7}{2}p+\frac{3}{4}a-\frac{21}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x+\frac{13}{15})(q-\frac{4}{20})& =(\color{red}{x}+\color{orange}{\frac{13}{15}}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{13}{15})} . \color{green}{(q)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{5}x+\frac{13}{15}q-\frac{13}{15}.\frac{1}{5}& \text{Uitwerken } \\ & =qx-\frac{1}{5}x+\frac{13}{15}q-\frac{13}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{5}{18})(b+\frac{-11}{6})& =(\color{red}{x}+\color{orange}{\frac{5}{18}}).(\color{green}{b}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{6}x+\frac{5}{18}b-\frac{5}{18}.\frac{11}{6}& \text{Uitwerken } \\ & =bx-\frac{11}{6}x+\frac{5}{18}b-\frac{55}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-11}{9}-a)(p+\frac{11}{3})& =(\color{red}{-a}+\color{orange}{\frac{-11}{9}}).(\color{green}{p}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{3}a-\frac{11}{9}p-\frac{11}{9}.\frac{11}{3}& \text{Uitwerken } \\ & =-ap-\frac{11}{3}a-\frac{11}{9}p-\frac{121}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)