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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-8}{6}-p)(\frac{15}{20}+b)& =(\color{red}{-p}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{4}p-\frac{4}{3}b-\frac{4}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =-bp-\frac{3}{4}p-\frac{4}{3}b-\frac{12}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{3}{4}p-\frac{4}{3}b-1 & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x+\frac{12}{16})(q-\frac{-17}{13})& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{q}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{13}x+\frac{3}{4}q+\frac{3}{4}.\frac{17}{13}& \text{Uitwerken } \\ & =qx+\frac{17}{13}x+\frac{3}{4}q+\frac{51}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-16}{2}-p)(\frac{-20}{9}-q)& =(\color{red}{-p}+\color{orange}{(-8)}).(\color{green}{-q}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(-8)} . \color{green}{(-q)} + \color{orange}{(-8)} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{20}{9}p+8q+8.\frac{20}{9}& \text{Uitwerken } \\ & =pq+\frac{20}{9}p+8q+\frac{160}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{16}{7}+p)(x+\frac{-16}{9})& =(\color{red}{p}+\color{orange}{\frac{16}{7}}).(\color{green}{x}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{16}{7})} . \color{green}{(x)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{16}{9}p+\frac{16}{7}x-\frac{16}{7}.\frac{16}{9}& \text{Uitwerken } \\ & =px-\frac{16}{9}p+\frac{16}{7}x-\frac{256}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{11}{6}+p)(\frac{18}{12}-b)& =(\color{red}{p}+\color{orange}{\frac{11}{6}}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{11}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{3}{2}p-\frac{11}{6}b+\frac{11}{6}.\frac{3}{2}& \text{Uitwerken } \\ & =-bp+\frac{3}{2}p-\frac{11}{6}b+\frac{33}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{3}{2}p-\frac{11}{6}b+\frac{11}{4} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b+\frac{20}{9})(\frac{18}{19}-b)& =(\color{red}{b}+\color{orange}{\frac{20}{9}}).(\color{green}{-b}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{20}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{18}{19}b-\frac{20}{9}b+\frac{20}{9}.\frac{18}{19}& \text{Uitwerken } \\ & =-b^2+(\frac{18}{19}+(\frac{-20}{9}))b+(\frac{-360}{171}) & \text{Neem samen} \\ &=-b^2-\frac{218}{171}b+(\frac{-360}{171}) & \text{Maak de som} \\ &=-b^2-\frac{218}{171}b+(\frac{-40}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(\frac{18}{13}+x)(p-\frac{-6}{12})& =(\color{red}{x}+\color{orange}{\frac{18}{13}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{18}{13})} . \color{green}{(p)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{2}x+\frac{18}{13}p+\frac{18}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =px+\frac{1}{2}x+\frac{18}{13}p+\frac{18}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{2}x+\frac{18}{13}p+\frac{9}{13} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-9}{2}+b)(\frac{-3}{13}-q)& =(\color{red}{b}+\color{orange}{\frac{-9}{2}}).(\color{green}{-q}+\color{blue}{\frac{-3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{13})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{-3}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{13}b+\frac{9}{2}q+\frac{9}{2}.\frac{3}{13}& \text{Uitwerken } \\ & =-bq-\frac{3}{13}b+\frac{9}{2}q+\frac{27}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+1)(13+x)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{x}+\color{blue}{13})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(13)} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = xx+13x+1x+1.13& \text{Uitwerken } \\ & =x^2+(13+1)x+13 & \text{Neem samen} \\ &=x^2+14x+13 & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(p-\frac{13}{6})(\frac{-14}{16}+x)& =(\color{red}{p}+\color{orange}{\frac{-13}{6}}).(\color{green}{x}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{8}p-\frac{13}{6}x+\frac{13}{6}.\frac{7}{8}& \text{Uitwerken } \\ & =px-\frac{7}{8}p-\frac{13}{6}x+\frac{91}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{8}{12}+q)(b-(-3))& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bq+3q+\frac{2}{3}b+\frac{2}{3}.3& \text{Uitwerken } \\ & =bq+3q+\frac{2}{3}b+\frac{6}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+3q+\frac{2}{3}b+2 & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{14}{18}-b)(x+\frac{8}{6})& =(\color{red}{-b}+\color{orange}{\frac{7}{9}}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{3}b+\frac{7}{9}x+\frac{7}{9}.\frac{4}{3}& \text{Uitwerken } \\ & =-bx-\frac{4}{3}b+\frac{7}{9}x+\frac{28}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)