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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{15}{19})(\frac{18}{5}+p)& =(\color{red}{p}+\color{orange}{\frac{-15}{19}}).(\color{green}{p}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{18}{5}p-\frac{15}{19}p-\frac{15}{19}.\frac{18}{5}& \text{Uitwerken } \\ & =p^2+(\frac{18}{5}+(\frac{-15}{19}))p-(\frac{-270}{95}) & \text{Neem samen} \\ &=p^2+\frac{267}{95}p-(\frac{-270}{95}) & \text{Maak de som} \\ &=p^2+\frac{267}{95}p+\frac{54}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
2. \(\begin{align}(\frac{2}{7}+x)(x-\frac{20}{19})& =(\color{red}{x}+\color{orange}{\frac{2}{7}}).(\color{green}{x}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{20}{19}x+\frac{2}{7}x-\frac{2}{7}.\frac{20}{19}& \text{Uitwerken } \\ & =x^2+((\frac{-20}{19})+\frac{2}{7})x-(\frac{-40}{133}) & \text{Neem samen} \\ &=x^2-\frac{102}{133}x-(\frac{-40}{133}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(x-\frac{2}{5})(b+\frac{18}{12})& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{2}x-\frac{2}{5}b-\frac{2}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =bx+\frac{3}{2}x-\frac{2}{5}b-\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{2}x-\frac{2}{5}b-\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{12}{8}-x)(\frac{2}{2}-q)& =(\color{red}{-x}+\color{orange}{\frac{3}{2}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx-1x-\frac{3}{2}q+\frac{3}{2}.1& \text{Uitwerken } \\ & =qx-1x-\frac{3}{2}q+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-16}{20}+b)(q+4)& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(4)} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bq+4b-\frac{4}{5}q-\frac{4}{5}.4& \text{Uitwerken } \\ & =bq+4b-\frac{4}{5}q-\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{8}{2})(x+11)& =(\color{red}{q}+\color{orange}{4}).(\color{green}{x}+\color{blue}{11})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(11)} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = qx+11q+4x+4.11& \text{Uitwerken } \\ & =qx+11q+4x+44 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q-\frac{5}{4})(\frac{-17}{4}-a)& =(\color{red}{q}+\color{orange}{\frac{-5}{4}}).(\color{green}{-a}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{17}{4}q+\frac{5}{4}a+\frac{5}{4}.\frac{17}{4}& \text{Uitwerken } \\ & =-aq-\frac{17}{4}q+\frac{5}{4}a+\frac{85}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{15}{11}+x)(b+\frac{19}{8})& =(\color{red}{x}+\color{orange}{\frac{15}{11}}).(\color{green}{b}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(\frac{15}{11})} . \color{green}{(b)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{8}x+\frac{15}{11}b+\frac{15}{11}.\frac{19}{8}& \text{Uitwerken } \\ & =bx+\frac{19}{8}x+\frac{15}{11}b+\frac{285}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(11-b)(\frac{-8}{9}+p)& =(\color{red}{-b}+\color{orange}{11}).(\color{green}{p}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(11)} . \color{green}{(p)} + \color{orange}{(11)} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{8}{9}b+11p-11.\frac{8}{9}& \text{Uitwerken } \\ & =-bp+\frac{8}{9}b+11p-\frac{88}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{7}{5}+x)(\frac{19}{9}+q)& =(\color{red}{x}+\color{orange}{\frac{7}{5}}).(\color{green}{q}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(\frac{7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{9}x+\frac{7}{5}q+\frac{7}{5}.\frac{19}{9}& \text{Uitwerken } \\ & =qx+\frac{19}{9}x+\frac{7}{5}q+\frac{133}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-\frac{-2}{10})(\frac{14}{11}-x)& =(\color{red}{x}+\color{orange}{\frac{1}{5}}).(\color{green}{-x}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{14}{11}x-\frac{1}{5}x+\frac{1}{5}.\frac{14}{11}& \text{Uitwerken } \\ & =-x^2+(\frac{14}{11}+(\frac{-1}{5}))x+(\frac{-14}{55}) & \text{Neem samen} \\ &=-x^2+\frac{59}{55}x+(\frac{-14}{55}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(p-\frac{14}{17})(\frac{-9}{9}+a)& =(\color{red}{p}+\color{orange}{\frac{-14}{17}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-14}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1p-\frac{14}{17}a+\frac{14}{17}.1& \text{Uitwerken } \\ & =ap-1p-\frac{14}{17}a+\frac{14}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)