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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-\frac{14}{14})(\frac{-11}{15}+p)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{15}x-1p+1.\frac{11}{15}& \text{Uitwerken } \\ & =px-\frac{11}{15}x-1p+\frac{11}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{-2}{10})(\frac{-16}{4}+b)& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{-1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bx-4x-\frac{1}{5}b+\frac{1}{5}.4& \text{Uitwerken } \\ & =bx-4x-\frac{1}{5}b+\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x+\frac{15}{4})(q-\frac{2}{5})& =(\color{red}{x}+\color{orange}{\frac{15}{4}}).(\color{green}{q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{15}{4})} . \color{green}{(q)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{5}x+\frac{15}{4}q-\frac{15}{4}.\frac{2}{5}& \text{Uitwerken } \\ & =qx-\frac{2}{5}x+\frac{15}{4}q-\frac{30}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{2}{5}x+\frac{15}{4}q-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{8}{19}+x)(\frac{-4}{11}+a)& =(\color{red}{x}+\color{orange}{\frac{8}{19}}).(\color{green}{a}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{8}{19})} . \color{green}{(a)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{11}x+\frac{8}{19}a-\frac{8}{19}.\frac{4}{11}& \text{Uitwerken } \\ & =ax-\frac{4}{11}x+\frac{8}{19}a-\frac{32}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{11}{5}-b)(\frac{-15}{12}-p)& =(\color{red}{-b}+\color{orange}{\frac{11}{5}}).(\color{green}{-p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{11}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{4}b-\frac{11}{5}p-\frac{11}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =bp+\frac{5}{4}b-\frac{11}{5}p-\frac{55}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{4}b-\frac{11}{5}p-\frac{11}{4} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-4}{14}-b)(\frac{9}{17}+q)& =(\color{red}{-b}+\color{orange}{\frac{-2}{7}}).(\color{green}{q}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{17}b-\frac{2}{7}q-\frac{2}{7}.\frac{9}{17}& \text{Uitwerken } \\ & =-bq-\frac{9}{17}b-\frac{2}{7}q-\frac{18}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{7}{15}+q)(\frac{6}{5}-x)& =(\color{red}{q}+\color{orange}{\frac{7}{15}}).(\color{green}{-x}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{7}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{6}{5}q-\frac{7}{15}x+\frac{7}{15}.\frac{6}{5}& \text{Uitwerken } \\ & =-qx+\frac{6}{5}q-\frac{7}{15}x+\frac{42}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{6}{5}q-\frac{7}{15}x+\frac{14}{25} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{5}{17}-b)(\frac{-1}{17}-b)& =(\color{red}{-b}+\color{orange}{\frac{5}{17}}).(\color{green}{-b}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{5}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{17}b-\frac{5}{17}b-\frac{5}{17}.\frac{1}{17}& \text{Uitwerken } \\ & =b^2+(\frac{1}{17}+(\frac{-5}{17}))b-(\frac{-5}{289}) & \text{Neem samen} \\ &=b^2-\frac{4}{17}b-(\frac{-5}{289}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(a+\frac{-12}{15})(\frac{9}{2}+b)& =(\color{red}{a}+\color{orange}{\frac{-4}{5}}).(\color{green}{b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{2}a-\frac{4}{5}b-\frac{4}{5}.\frac{9}{2}& \text{Uitwerken } \\ & =ab+\frac{9}{2}a-\frac{4}{5}b-\frac{36}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{9}{2}a-\frac{4}{5}b-\frac{18}{5} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-12}{9}+q)(\frac{-9}{6}-a)& =(\color{red}{q}+\color{orange}{\frac{-4}{3}}).(\color{green}{-a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{2}q+\frac{4}{3}a+\frac{4}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =-aq-\frac{3}{2}q+\frac{4}{3}a+\frac{12}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{3}{2}q+\frac{4}{3}a+2 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-3}{17}-q)(p+\frac{2}{14})& =(\color{red}{-q}+\color{orange}{\frac{-3}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-3}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{7}q-\frac{3}{17}p-\frac{3}{17}.\frac{1}{7}& \text{Uitwerken } \\ & =-pq-\frac{1}{7}q-\frac{3}{17}p-\frac{3}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{-17}{10})(q+\frac{-15}{10})& =(\color{red}{q}+\color{orange}{\frac{17}{10}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{17}{10})} . \color{green}{(q)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{2}q+\frac{17}{10}q-\frac{17}{10}.\frac{3}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{2})+\frac{17}{10})q-(\frac{-51}{20}) & \text{Neem samen} \\ &=q^2+\frac{2}{10}q-(\frac{-51}{20}) & \text{Maak de som} \\ &=q^2+\frac{1}{5}q+\frac{51}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)