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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-\frac{-4}{15})(\frac{-2}{17}+x)& =(\color{red}{x}+\color{orange}{\frac{4}{15}}).(\color{green}{x}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{4}{15})} . \color{green}{(x)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{2}{17}x+\frac{4}{15}x-\frac{4}{15}.\frac{2}{17}& \text{Uitwerken } \\ & =x^2+((\frac{-2}{17})+\frac{4}{15})x-(\frac{-8}{255}) & \text{Neem samen} \\ &=x^2+\frac{38}{255}x-(\frac{-8}{255}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{8}{3}-x)(\frac{18}{5}+q)& =(\color{red}{-x}+\color{orange}{\frac{8}{3}}).(\color{green}{q}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{18}{5}x+\frac{8}{3}q+\frac{8}{3}.\frac{18}{5}& \text{Uitwerken } \\ & =-qx-\frac{18}{5}x+\frac{8}{3}q+\frac{144}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{18}{5}x+\frac{8}{3}q+\frac{48}{5} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(p+\frac{16}{16})(p-\frac{10}{18})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{9}p+1p-1.\frac{5}{9}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{9})+1)p-(\frac{-5}{9}) & \text{Neem samen} \\ &=p^2+\frac{4}{9}p-(\frac{-5}{9}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(q-\frac{6}{12})(x-\frac{-2}{5})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{5}q-\frac{1}{2}x-\frac{1}{2}.\frac{2}{5}& \text{Uitwerken } \\ & =qx+\frac{2}{5}q-\frac{1}{2}x-\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{2}{5}q-\frac{1}{2}x-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-8}{20}+b)(\frac{19}{18}+b)& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{\frac{19}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{19}{18})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{19}{18})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{19}{18}b-\frac{2}{5}b-\frac{2}{5}.\frac{19}{18}& \text{Uitwerken } \\ & =b^2+(\frac{19}{18}+(\frac{-2}{5}))b-(\frac{-38}{90}) & \text{Neem samen} \\ &=b^2+\frac{59}{90}b-(\frac{-38}{90}) & \text{Maak de som} \\ &=b^2+\frac{59}{90}b+\frac{19}{45} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
6. \(\begin{align}(\frac{-12}{8}-q)(\frac{-13}{18}-x)& =(\color{red}{-q}+\color{orange}{\frac{-3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{18}q+\frac{3}{2}x+\frac{3}{2}.\frac{13}{18}& \text{Uitwerken } \\ & =qx+\frac{13}{18}q+\frac{3}{2}x+\frac{39}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{13}{18}q+\frac{3}{2}x+\frac{13}{12} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b+\frac{1}{2})(\frac{-6}{4}+x)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{2}b+\frac{1}{2}x-\frac{1}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =bx-\frac{3}{2}b+\frac{1}{2}x-\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{18}{14}-x)(\frac{-12}{6}+b)& =(\color{red}{-x}+\color{orange}{\frac{9}{7}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(-2)} + \color{orange}{(\frac{9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bx+2x+\frac{9}{7}b-\frac{9}{7}.2& \text{Uitwerken } \\ & =-bx+2x+\frac{9}{7}b-\frac{18}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-19}{9}-b)(\frac{8}{11}-q)& =(\color{red}{-b}+\color{orange}{\frac{-19}{9}}).(\color{green}{-q}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{11}b+\frac{19}{9}q-\frac{19}{9}.\frac{8}{11}& \text{Uitwerken } \\ & =bq-\frac{8}{11}b+\frac{19}{9}q-\frac{152}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{-15}{12})(\frac{-6}{18}+b)& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{3}a-\frac{5}{4}b+\frac{5}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =ab-\frac{1}{3}a-\frac{5}{4}b+\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{16}{12}+q)(p+\frac{12}{2})& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = pq+6q+\frac{4}{3}p+\frac{4}{3}.6& \text{Uitwerken } \\ & =pq+6q+\frac{4}{3}p+\frac{24}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+6q+\frac{4}{3}p+8 & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q+\frac{9}{3})(x-\frac{-18}{2})& =(\color{red}{q}+\color{orange}{3}).(\color{green}{x}+\color{blue}{9})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(9)} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = qx+9q+3x+3.9& \text{Uitwerken } \\ & =qx+9q+3x+27 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)