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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-8}{11})(\frac{-18}{3}+x)& =(\color{red}{p}+\color{orange}{\frac{8}{11}}).(\color{green}{x}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-6)} + \color{orange}{(\frac{8}{11})} . \color{green}{(x)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = px-6p+\frac{8}{11}x-\frac{8}{11}.6& \text{Uitwerken } \\ & =px-6p+\frac{8}{11}x-\frac{48}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-18}{6}-x)(\frac{9}{10}-b)& =(\color{red}{-x}+\color{orange}{(-3)}).(\color{green}{-b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(-3)} . \color{green}{(-b)} + \color{orange}{(-3)} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{10}x+3b-3.\frac{9}{10}& \text{Uitwerken } \\ & =bx-\frac{9}{10}x+3b-\frac{27}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a+\frac{-10}{18})(\frac{-19}{9}+a)& =(\color{red}{a}+\color{orange}{\frac{-5}{9}}).(\color{green}{a}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{19}{9}a-\frac{5}{9}a+\frac{5}{9}.\frac{19}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-19}{9})+(\frac{-5}{9}))a+\frac{95}{81} & \text{Neem samen} \\ &=a^2-\frac{24}{9}a+\frac{95}{81} & \text{Maak de som} \\ &=a^2-\frac{8}{3}a+\frac{95}{81} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(\frac{8}{4}-p)(\frac{9}{6}-a)& =(\color{red}{-p}+\color{orange}{2}).(\color{green}{-a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(2)} . \color{green}{(-a)} + \color{orange}{(2)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{2}p-2a+2.\frac{3}{2}& \text{Uitwerken } \\ & =ap-\frac{3}{2}p-2a+\frac{6}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{3}{2}p-2a+3 & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-6}{11}+q)(a-\frac{-6}{13})& =(\color{red}{q}+\color{orange}{\frac{-6}{11}}).(\color{green}{a}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{13}q-\frac{6}{11}a-\frac{6}{11}.\frac{6}{13}& \text{Uitwerken } \\ & =aq+\frac{6}{13}q-\frac{6}{11}a-\frac{36}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b-\frac{7}{13})(12+q)& =(\color{red}{b}+\color{orange}{\frac{-7}{13}}).(\color{green}{q}+\color{blue}{12})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(12)} + \color{orange}{(\frac{-7}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = bq+12b-\frac{7}{13}q-\frac{7}{13}.12& \text{Uitwerken } \\ & =bq+12b-\frac{7}{13}q-\frac{84}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b-14)(q-\frac{-6}{6})& =(\color{red}{b}+\color{orange}{(-14)}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(-14)} . \color{green}{(q)} + \color{orange}{(-14)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b-14q-14.1& \text{Uitwerken } \\ & =bq+1b-14q-14 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{16}{12}-a)(q+\frac{-14}{4})& =(\color{red}{-a}+\color{orange}{\frac{4}{3}}).(\color{green}{q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{2}a+\frac{4}{3}q-\frac{4}{3}.\frac{7}{2}& \text{Uitwerken } \\ & =-aq+\frac{7}{2}a+\frac{4}{3}q-\frac{28}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{7}{2}a+\frac{4}{3}q-\frac{14}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-7}{6}+q)(x+\frac{7}{9})& =(\color{red}{q}+\color{orange}{\frac{-7}{6}}).(\color{green}{x}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{9}q-\frac{7}{6}x-\frac{7}{6}.\frac{7}{9}& \text{Uitwerken } \\ & =qx+\frac{7}{9}q-\frac{7}{6}x-\frac{49}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{4}{2}+b)(\frac{3}{17}-x)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{-x}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(2)} . \color{green}{(-x)} + \color{orange}{(2)} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{17}b-2x+2.\frac{3}{17}& \text{Uitwerken } \\ & =-bx+\frac{3}{17}b-2x+\frac{6}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{12}{5}+p)(q-\frac{-9}{9})& =(\color{red}{p}+\color{orange}{\frac{12}{5}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{12}{5})} . \color{green}{(q)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p+\frac{12}{5}q+\frac{12}{5}.1& \text{Uitwerken } \\ & =pq+1p+\frac{12}{5}q+\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{20}{8})(\frac{-12}{15}-p)& =(\color{red}{q}+\color{orange}{\frac{5}{2}}).(\color{green}{-p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{5}q-\frac{5}{2}p-\frac{5}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =-pq-\frac{4}{5}q-\frac{5}{2}p-\frac{20}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{4}{5}q-\frac{5}{2}p-2 & \text{Vereenvoudig} \\\end{align}\)