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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{17}{12}-a)(\frac{-18}{2}+q)& =(\color{red}{-a}+\color{orange}{\frac{17}{12}}).(\color{green}{q}+\color{blue}{(-9)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(-9)} + \color{orange}{(\frac{17}{12})} . \color{green}{(q)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -aq+9a+\frac{17}{12}q-\frac{17}{12}.9& \text{Uitwerken } \\ & =-aq+9a+\frac{17}{12}q-\frac{153}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+9a+\frac{17}{12}q-\frac{51}{4} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p+\frac{13}{10})(\frac{-5}{11}+q)& =(\color{red}{p}+\color{orange}{\frac{13}{10}}).(\color{green}{q}+\color{blue}{\frac{-5}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{11})} + \color{orange}{(\frac{13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{-5}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{11}p+\frac{13}{10}q-\frac{13}{10}.\frac{5}{11}& \text{Uitwerken } \\ & =pq-\frac{5}{11}p+\frac{13}{10}q-\frac{65}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{5}{11}p+\frac{13}{10}q-\frac{13}{22} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}((-11)-a)(\frac{-20}{3}-b)& =(\color{red}{-a}+\color{orange}{(-11)}).(\color{green}{-b}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(-11)} . \color{green}{(-b)} + \color{orange}{(-11)} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{20}{3}a+11b+11.\frac{20}{3}& \text{Uitwerken } \\ & =ab+\frac{20}{3}a+11b+\frac{220}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}((-17)-a)(\frac{-12}{9}+q)& =(\color{red}{-a}+\color{orange}{(-17)}).(\color{green}{q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(-17)} . \color{green}{(q)} + \color{orange}{(-17)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{4}{3}a-17q+17.\frac{4}{3}& \text{Uitwerken } \\ & =-aq+\frac{4}{3}a-17q+\frac{68}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{15}{17}+q)(\frac{16}{10}+p)& =(\color{red}{q}+\color{orange}{\frac{15}{17}}).(\color{green}{p}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{15}{17})} . \color{green}{(p)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{5}q+\frac{15}{17}p+\frac{15}{17}.\frac{8}{5}& \text{Uitwerken } \\ & =pq+\frac{8}{5}q+\frac{15}{17}p+\frac{120}{85} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{8}{5}q+\frac{15}{17}p+\frac{24}{17} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(a+\frac{5}{14})(\frac{-4}{8}+b)& =(\color{red}{a}+\color{orange}{\frac{5}{14}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{5}{14})} . \color{green}{(b)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{2}a+\frac{5}{14}b-\frac{5}{14}.\frac{1}{2}& \text{Uitwerken } \\ & =ab-\frac{1}{2}a+\frac{5}{14}b-\frac{5}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{2}{4})(q-\frac{2}{8})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{4}q+\frac{1}{2}q-\frac{1}{2}.\frac{1}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{4})+\frac{1}{2})q-(\frac{-1}{8}) & \text{Neem samen} \\ &=q^2+\frac{1}{4}q-(\frac{-1}{8}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(a+\frac{-18}{5})(\frac{18}{10}-b)& =(\color{red}{a}+\color{orange}{\frac{-18}{5}}).(\color{green}{-b}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{9}{5}a+\frac{18}{5}b-\frac{18}{5}.\frac{9}{5}& \text{Uitwerken } \\ & =-ab+\frac{9}{5}a+\frac{18}{5}b-\frac{162}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{-1}{5})(q+\frac{1}{7})& =(\color{red}{a}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{7}a+\frac{1}{5}q+\frac{1}{5}.\frac{1}{7}& \text{Uitwerken } \\ & =aq+\frac{1}{7}a+\frac{1}{5}q+\frac{1}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b+\frac{16}{20})(\frac{-10}{8}-q)& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{-q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{4}b-\frac{4}{5}q-\frac{4}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =-bq-\frac{5}{4}b-\frac{4}{5}q-\frac{20}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{5}{4}b-\frac{4}{5}q-1 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-2}{5}+x)(\frac{-20}{5}-x)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{-x}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -xx-4x+\frac{2}{5}x+\frac{2}{5}.4& \text{Uitwerken } \\ & =-x^2+((-4)+\frac{2}{5})x+(\frac{-8}{5}) & \text{Neem samen} \\ &=-x^2-\frac{18}{5}x+(\frac{-8}{5}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-7}{14}-a)(x+\frac{-14}{7})& =(\color{red}{-a}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ax+2a-\frac{1}{2}x+\frac{1}{2}.2& \text{Uitwerken } \\ & =-ax+2a-\frac{1}{2}x+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+2a-\frac{1}{2}x+1 & \text{Vereenvoudig} \\\end{align}\)