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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-6}{7}+p)(\frac{-1}{11}+b)& =(\color{red}{p}+\color{orange}{\frac{-6}{7}}).(\color{green}{b}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{11}p-\frac{6}{7}b+\frac{6}{7}.\frac{1}{11}& \text{Uitwerken } \\ & =bp-\frac{1}{11}p-\frac{6}{7}b+\frac{6}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-19}{4}-x)(q+\frac{3}{17})& =(\color{red}{-x}+\color{orange}{\frac{-19}{4}}).(\color{green}{q}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-19}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{4})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{17}x-\frac{19}{4}q-\frac{19}{4}.\frac{3}{17}& \text{Uitwerken } \\ & =-qx-\frac{3}{17}x-\frac{19}{4}q-\frac{57}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-1}{3}-x)(\frac{15}{3}-q)& =(\color{red}{-x}+\color{orange}{\frac{-1}{3}}).(\color{green}{-q}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(5)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = qx-5x+\frac{1}{3}q-\frac{1}{3}.5& \text{Uitwerken } \\ & =qx-5x+\frac{1}{3}q-\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a+\frac{13}{4})(p+\frac{-3}{3})& =(\color{red}{a}+\color{orange}{\frac{13}{4}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{4})} . \color{green}{(p)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a+\frac{13}{4}p-\frac{13}{4}.1& \text{Uitwerken } \\ & =ap-1a+\frac{13}{4}p-\frac{13}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{7}{3})(p+\frac{15}{15})& =(\color{red}{x}+\color{orange}{\frac{-7}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-7}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1x-\frac{7}{3}p-\frac{7}{3}.1& \text{Uitwerken } \\ & =px+1x-\frac{7}{3}p-\frac{7}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q-\frac{-18}{8})(\frac{-6}{14}-x)& =(\color{red}{q}+\color{orange}{\frac{9}{4}}).(\color{green}{-x}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{9}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{7}q-\frac{9}{4}x-\frac{9}{4}.\frac{3}{7}& \text{Uitwerken } \\ & =-qx-\frac{3}{7}q-\frac{9}{4}x-\frac{27}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-12}{4}-x)(x-\frac{-12}{12})& =(\color{red}{-x}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -xx-1x-3x-3.1& \text{Uitwerken } \\ & =-x^2+((-1)+(-3))x-3 & \text{Neem samen} \\ &=-x^2-4x-3 & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{6}{9}+b)(\frac{14}{12}-b)& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{-b}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{7}{6}b-\frac{2}{3}b+\frac{2}{3}.\frac{7}{6}& \text{Uitwerken } \\ & =-b^2+(\frac{7}{6}+(\frac{-2}{3}))b+(\frac{-14}{18}) & \text{Neem samen} \\ &=-b^2+\frac{3}{6}b+(\frac{-14}{18}) & \text{Maak de som} \\ &=-b^2+\frac{1}{2}b+(\frac{-7}{9}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(\frac{-17}{3}-p)(\frac{20}{7}+b)& =(\color{red}{-p}+\color{orange}{\frac{-17}{3}}).(\color{green}{b}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{20}{7}p-\frac{17}{3}b-\frac{17}{3}.\frac{20}{7}& \text{Uitwerken } \\ & =-bp-\frac{20}{7}p-\frac{17}{3}b-\frac{340}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-4}{7}+a)(\frac{-3}{10}-x)& =(\color{red}{a}+\color{orange}{\frac{-4}{7}}).(\color{green}{-x}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{10}a+\frac{4}{7}x+\frac{4}{7}.\frac{3}{10}& \text{Uitwerken } \\ & =-ax-\frac{3}{10}a+\frac{4}{7}x+\frac{12}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{3}{10}a+\frac{4}{7}x+\frac{6}{35} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-16}{16}-a)(\frac{-15}{17}+a)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{15}{17}a-1a+1.\frac{15}{17}& \text{Uitwerken } \\ & =-a^2+(\frac{15}{17}+(-1))a+(\frac{-15}{17}) & \text{Neem samen} \\ &=-a^2-\frac{2}{17}a+(\frac{-15}{17}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(q-\frac{-3}{15})(\frac{-12}{12}-q)& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qq-1q-\frac{1}{5}q-\frac{1}{5}.1& \text{Uitwerken } \\ & =-q^2+((-1)+(\frac{-1}{5}))q-\frac{1}{5} & \text{Neem samen} \\ &=-q^2-\frac{6}{5}q-\frac{1}{5} & \text{Maak de som} \\\end{align}\)