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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-2}{14}+b)(\frac{2}{14}-p)& =(\color{red}{b}+\color{orange}{\frac{-1}{7}}).(\color{green}{-p}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{7}b+\frac{1}{7}p-\frac{1}{7}.\frac{1}{7}& \text{Uitwerken } \\ & =-bp+\frac{1}{7}b+\frac{1}{7}p-\frac{1}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{12}{20}-x)(a-\frac{9}{18})& =(\color{red}{-x}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{2}x+\frac{3}{5}a-\frac{3}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-ax+\frac{1}{2}x+\frac{3}{5}a-\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-9}{6}+q)(\frac{1}{18}+p)& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{18}q-\frac{3}{2}p-\frac{3}{2}.\frac{1}{18}& \text{Uitwerken } \\ & =pq+\frac{1}{18}q-\frac{3}{2}p-\frac{3}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{18}q-\frac{3}{2}p-\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-17}{10}+q)(\frac{20}{9}-q)& =(\color{red}{q}+\color{orange}{\frac{-17}{10}}).(\color{green}{-q}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{20}{9}q+\frac{17}{10}q-\frac{17}{10}.\frac{20}{9}& \text{Uitwerken } \\ & =-q^2+(\frac{20}{9}+\frac{17}{10})q-\frac{340}{90} & \text{Neem samen} \\ &=-q^2+\frac{353}{90}q-\frac{340}{90} & \text{Maak de som} \\ &=-q^2+\frac{353}{90}q-\frac{34}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(\frac{-1}{19}+b)(x-(-14))& =(\color{red}{b}+\color{orange}{\frac{-1}{19}}).(\color{green}{x}+\color{blue}{14})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(14)} + \color{orange}{(\frac{-1}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = bx+14b-\frac{1}{19}x-\frac{1}{19}.14& \text{Uitwerken } \\ & =bx+14b-\frac{1}{19}x-\frac{14}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-18}{7}-a)(\frac{-4}{9}-q)& =(\color{red}{-a}+\color{orange}{\frac{-18}{7}}).(\color{green}{-q}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{9}a+\frac{18}{7}q+\frac{18}{7}.\frac{4}{9}& \text{Uitwerken } \\ & =aq+\frac{4}{9}a+\frac{18}{7}q+\frac{72}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{4}{9}a+\frac{18}{7}q+\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(p+\frac{4}{6})(\frac{-14}{13}+x)& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{14}{13}p+\frac{2}{3}x-\frac{2}{3}.\frac{14}{13}& \text{Uitwerken } \\ & =px-\frac{14}{13}p+\frac{2}{3}x-\frac{28}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{-3}{7})(\frac{13}{2}-a)& =(\color{red}{p}+\color{orange}{\frac{-3}{7}}).(\color{green}{-a}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{2}p+\frac{3}{7}a-\frac{3}{7}.\frac{13}{2}& \text{Uitwerken } \\ & =-ap+\frac{13}{2}p+\frac{3}{7}a-\frac{39}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{17}{14}+x)(\frac{-18}{19}+q)& =(\color{red}{x}+\color{orange}{\frac{17}{14}}).(\color{green}{q}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{17}{14})} . \color{green}{(q)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{18}{19}x+\frac{17}{14}q-\frac{17}{14}.\frac{18}{19}& \text{Uitwerken } \\ & =qx-\frac{18}{19}x+\frac{17}{14}q-\frac{306}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{18}{19}x+\frac{17}{14}q-\frac{153}{133} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a-\frac{17}{16})(q+\frac{16}{9})& =(\color{red}{a}+\color{orange}{\frac{-17}{16}}).(\color{green}{q}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{16}{9}a-\frac{17}{16}q-\frac{17}{16}.\frac{16}{9}& \text{Uitwerken } \\ & =aq+\frac{16}{9}a-\frac{17}{16}q-\frac{272}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{16}{9}a-\frac{17}{16}q-\frac{17}{9} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-19}{4}-q)(p+\frac{18}{13})& =(\color{red}{-q}+\color{orange}{\frac{-19}{4}}).(\color{green}{p}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{-19}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{4})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{18}{13}q-\frac{19}{4}p-\frac{19}{4}.\frac{18}{13}& \text{Uitwerken } \\ & =-pq-\frac{18}{13}q-\frac{19}{4}p-\frac{342}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{18}{13}q-\frac{19}{4}p-\frac{171}{26} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-14}{11}+q)(\frac{7}{19}-x)& =(\color{red}{q}+\color{orange}{\frac{-14}{11}}).(\color{green}{-x}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{7}{19}q+\frac{14}{11}x-\frac{14}{11}.\frac{7}{19}& \text{Uitwerken } \\ & =-qx+\frac{7}{19}q+\frac{14}{11}x-\frac{98}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)