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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{20}{4})(\frac{7}{3}-a)& =(\color{red}{q}+\color{orange}{(-5)}).(\color{green}{-a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(-5)} . \color{green}{(-a)} + \color{orange}{(-5)} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{3}q+5a-5.\frac{7}{3}& \text{Uitwerken } \\ & =-aq+\frac{7}{3}q+5a-\frac{35}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p+\frac{-18}{16})(\frac{3}{5}+q)& =(\color{red}{p}+\color{orange}{\frac{-9}{8}}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{5}p-\frac{9}{8}q-\frac{9}{8}.\frac{3}{5}& \text{Uitwerken } \\ & =pq+\frac{3}{5}p-\frac{9}{8}q-\frac{27}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-2}{3}+q)(x+19)& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{19})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(19)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = qx+19q-\frac{2}{3}x-\frac{2}{3}.19& \text{Uitwerken } \\ & =qx+19q-\frac{2}{3}x-\frac{38}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-11}{13}+p)(\frac{7}{11}+p)& =(\color{red}{p}+\color{orange}{\frac{-11}{13}}).(\color{green}{p}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{11}p-\frac{11}{13}p-\frac{11}{13}.\frac{7}{11}& \text{Uitwerken } \\ & =p^2+(\frac{7}{11}+(\frac{-11}{13}))p-(\frac{-77}{143}) & \text{Neem samen} \\ &=p^2-\frac{30}{143}p-(\frac{-77}{143}) & \text{Maak de som} \\ &=p^2-\frac{30}{143}p+\frac{7}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
5. \(\begin{align}(\frac{20}{11}+q)(q+\frac{11}{12})& =(\color{red}{q}+\color{orange}{\frac{20}{11}}).(\color{green}{q}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{20}{11})} . \color{green}{(q)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{11}{12}q+\frac{20}{11}q+\frac{20}{11}.\frac{11}{12}& \text{Uitwerken } \\ & =q^2+(\frac{11}{12}+\frac{20}{11})q+\frac{220}{132} & \text{Neem samen} \\ &=q^2+\frac{361}{132}q+\frac{220}{132} & \text{Maak de som} \\ &=q^2+\frac{361}{132}q+\frac{5}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
6. \(\begin{align}(p-14)(\frac{-8}{12}-x)& =(\color{red}{p}+\color{orange}{(-14)}).(\color{green}{-x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-14)} . \color{green}{(-x)} + \color{orange}{(-14)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{3}p+14x+14.\frac{2}{3}& \text{Uitwerken } \\ & =-px-\frac{2}{3}p+14x+\frac{28}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{-11}{10})(x-\frac{15}{15})& =(\color{red}{q}+\color{orange}{\frac{-11}{10}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-11}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q-\frac{11}{10}x+\frac{11}{10}.1& \text{Uitwerken } \\ & =qx-1q-\frac{11}{10}x+\frac{11}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a+\frac{4}{10})(x-\frac{18}{18})& =(\color{red}{a}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a+\frac{2}{5}x-\frac{2}{5}.1& \text{Uitwerken } \\ & =ax-1a+\frac{2}{5}x-\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{19}{11}+p)(q-\frac{-15}{16})& =(\color{red}{p}+\color{orange}{\frac{19}{11}}).(\color{green}{q}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{19}{11})} . \color{green}{(q)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{15}{16}p+\frac{19}{11}q+\frac{19}{11}.\frac{15}{16}& \text{Uitwerken } \\ & =pq+\frac{15}{16}p+\frac{19}{11}q+\frac{285}{176} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{7}{2}+b)(b-\frac{-11}{5})& =(\color{red}{b}+\color{orange}{\frac{7}{2}}).(\color{green}{b}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{11}{5}b+\frac{7}{2}b+\frac{7}{2}.\frac{11}{5}& \text{Uitwerken } \\ & =b^2+(\frac{11}{5}+\frac{7}{2})b+\frac{77}{10} & \text{Neem samen} \\ &=b^2+\frac{57}{10}b+\frac{77}{10} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-7}{13}+q)(\frac{-20}{10}+p)& =(\color{red}{q}+\color{orange}{\frac{-7}{13}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2q-\frac{7}{13}p+\frac{7}{13}.2& \text{Uitwerken } \\ & =pq-2q-\frac{7}{13}p+\frac{14}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{5}{5})(x+\frac{2}{13})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{13}b+1x+1.\frac{2}{13}& \text{Uitwerken } \\ & =bx+\frac{2}{13}b+1x+\frac{2}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)