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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-(-18))(p-\frac{14}{19})& =(\color{red}{x}+\color{orange}{18}).(\color{green}{p}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(18)} . \color{green}{(p)} + \color{orange}{(18)} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{14}{19}x+18p-18.\frac{14}{19}& \text{Uitwerken } \\ & =px-\frac{14}{19}x+18p-\frac{252}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p+\frac{-15}{4})(b+\frac{-18}{8})& =(\color{red}{p}+\color{orange}{\frac{-15}{4}}).(\color{green}{b}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{4}p-\frac{15}{4}b+\frac{15}{4}.\frac{9}{4}& \text{Uitwerken } \\ & =bp-\frac{9}{4}p-\frac{15}{4}b+\frac{135}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-2}{10}+q)(\frac{-14}{9}-a)& =(\color{red}{q}+\color{orange}{\frac{-1}{5}}).(\color{green}{-a}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{14}{9}q+\frac{1}{5}a+\frac{1}{5}.\frac{14}{9}& \text{Uitwerken } \\ & =-aq-\frac{14}{9}q+\frac{1}{5}a+\frac{14}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{9}{3}-b)(\frac{-15}{5}-p)& =(\color{red}{-b}+\color{orange}{3}).(\color{green}{-p}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(-3)} + \color{orange}{(3)} . \color{green}{(-p)} + \color{orange}{(3)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bp+3b-3p-3.3& \text{Uitwerken } \\ & =bp+3b-3p-9 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-17}{14}+b)(\frac{-2}{3}-p)& =(\color{red}{b}+\color{orange}{\frac{-17}{14}}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{2}{3}b+\frac{17}{14}p+\frac{17}{14}.\frac{2}{3}& \text{Uitwerken } \\ & =-bp-\frac{2}{3}b+\frac{17}{14}p+\frac{34}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{2}{3}b+\frac{17}{14}p+\frac{17}{21} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{15}{13}-b)(\frac{-6}{13}-x)& =(\color{red}{-b}+\color{orange}{\frac{15}{13}}).(\color{green}{-x}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{15}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{6}{13}b-\frac{15}{13}x-\frac{15}{13}.\frac{6}{13}& \text{Uitwerken } \\ & =bx+\frac{6}{13}b-\frac{15}{13}x-\frac{90}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-6}{3}-q)(q-\frac{11}{18})& =(\color{red}{-q}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{11}{18}q-2q+2.\frac{11}{18}& \text{Uitwerken } \\ & =-q^2+(\frac{11}{18}+(-2))q+(\frac{-22}{18}) & \text{Neem samen} \\ &=-q^2-\frac{25}{18}q+(\frac{-22}{18}) & \text{Maak de som} \\ &=-q^2-\frac{25}{18}q+(\frac{-11}{9}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(x-\frac{1}{10})(x-(-15))& =(\color{red}{x}+\color{orange}{\frac{-1}{10}}).(\color{green}{x}+\color{blue}{15})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(15)} + \color{orange}{(\frac{-1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(15)}& \text{Boogjes en uitschrijven} \\ & = xx+15x-\frac{1}{10}x-\frac{1}{10}.15& \text{Uitwerken } \\ & =x^2+(15+(\frac{-1}{10}))x-(\frac{-15}{10}) & \text{Neem samen} \\ &=x^2+\frac{149}{10}x-(\frac{-15}{10}) & \text{Maak de som} \\ &=x^2+\frac{149}{10}x+\frac{3}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
9. \(\begin{align}(p+\frac{-10}{14})(\frac{-7}{2}+q)& =(\color{red}{p}+\color{orange}{\frac{-5}{7}}).(\color{green}{q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{2}p-\frac{5}{7}q+\frac{5}{7}.\frac{7}{2}& \text{Uitwerken } \\ & =pq-\frac{7}{2}p-\frac{5}{7}q+\frac{35}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{7}{2}p-\frac{5}{7}q+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q-\frac{2}{8})(x+\frac{20}{12})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{x}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{3}q-\frac{1}{4}x-\frac{1}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =qx+\frac{5}{3}q-\frac{1}{4}x-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{3}{9})(\frac{2}{3}-q)& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{-q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{2}{3}p+\frac{1}{3}q-\frac{1}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-pq+\frac{2}{3}p+\frac{1}{3}q-\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-4}{3}+a)(a-\frac{5}{9})& =(\color{red}{a}+\color{orange}{\frac{-4}{3}}).(\color{green}{a}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{9}a-\frac{4}{3}a+\frac{4}{3}.\frac{5}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{9})+(\frac{-4}{3}))a+\frac{20}{27} & \text{Neem samen} \\ &=a^2-\frac{17}{9}a+\frac{20}{27} & \text{Maak de som} \\\end{align}\)