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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{5}{18})(p-\frac{-14}{18})& =(\color{red}{a}+\color{orange}{\frac{-5}{18}}).(\color{green}{p}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{9}a-\frac{5}{18}p-\frac{5}{18}.\frac{7}{9}& \text{Uitwerken } \\ & =ap+\frac{7}{9}a-\frac{5}{18}p-\frac{35}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{-6}{10})(x-\frac{-3}{18})& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{6}q+\frac{3}{5}x+\frac{3}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =qx+\frac{1}{6}q+\frac{3}{5}x+\frac{3}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{6}q+\frac{3}{5}x+\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q+\frac{-17}{13})(q-\frac{-8}{20})& =(\color{red}{q}+\color{orange}{\frac{-17}{13}}).(\color{green}{q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-17}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{2}{5}q-\frac{17}{13}q-\frac{17}{13}.\frac{2}{5}& \text{Uitwerken } \\ & =q^2+(\frac{2}{5}+(\frac{-17}{13}))q-(\frac{-34}{65}) & \text{Neem samen} \\ &=q^2-\frac{59}{65}q-(\frac{-34}{65}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(x-\frac{-4}{15})(\frac{10}{5}-p)& =(\color{red}{x}+\color{orange}{\frac{4}{15}}).(\color{green}{-p}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{4}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -px+2x-\frac{4}{15}p+\frac{4}{15}.2& \text{Uitwerken } \\ & =-px+2x-\frac{4}{15}p+\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{6}{12}-x)(\frac{5}{18}+b)& =(\color{red}{-x}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{18}x+\frac{1}{2}b+\frac{1}{2}.\frac{5}{18}& \text{Uitwerken } \\ & =-bx-\frac{5}{18}x+\frac{1}{2}b+\frac{5}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{4}{3}+a)(b+\frac{12}{17})& =(\color{red}{a}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{12}{17}a+\frac{4}{3}b+\frac{4}{3}.\frac{12}{17}& \text{Uitwerken } \\ & =ab+\frac{12}{17}a+\frac{4}{3}b+\frac{48}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{12}{17}a+\frac{4}{3}b+\frac{16}{17} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-2}{11}-q)(\frac{14}{7}-q)& =(\color{red}{-q}+\color{orange}{\frac{-2}{11}}).(\color{green}{-q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{-2}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qq-2q+\frac{2}{11}q-\frac{2}{11}.2& \text{Uitwerken } \\ & =q^2+((-2)+\frac{2}{11})q-(\frac{-4}{11}) & \text{Neem samen} \\ &=q^2-\frac{20}{11}q-(\frac{-4}{11}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(a+\frac{-12}{15})(\frac{-1}{17}-b)& =(\color{red}{a}+\color{orange}{\frac{-4}{5}}).(\color{green}{-b}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{17}a+\frac{4}{5}b+\frac{4}{5}.\frac{1}{17}& \text{Uitwerken } \\ & =-ab-\frac{1}{17}a+\frac{4}{5}b+\frac{4}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{-10}{13})(\frac{-3}{7}+x)& =(\color{red}{x}+\color{orange}{\frac{-10}{13}}).(\color{green}{x}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{7}x-\frac{10}{13}x+\frac{10}{13}.\frac{3}{7}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{7})+(\frac{-10}{13}))x+\frac{30}{91} & \text{Neem samen} \\ &=x^2-\frac{109}{91}x+\frac{30}{91} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(a-\frac{-17}{5})(\frac{-3}{11}-q)& =(\color{red}{a}+\color{orange}{\frac{17}{5}}).(\color{green}{-q}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{17}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{11}a-\frac{17}{5}q-\frac{17}{5}.\frac{3}{11}& \text{Uitwerken } \\ & =-aq-\frac{3}{11}a-\frac{17}{5}q-\frac{51}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{-9}{19})(\frac{-14}{5}+x)& =(\color{red}{q}+\color{orange}{\frac{9}{19}}).(\color{green}{x}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{9}{19})} . \color{green}{(x)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{5}q+\frac{9}{19}x-\frac{9}{19}.\frac{14}{5}& \text{Uitwerken } \\ & =qx-\frac{14}{5}q+\frac{9}{19}x-\frac{126}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p-\frac{-9}{13})(\frac{14}{20}+q)& =(\color{red}{p}+\color{orange}{\frac{9}{13}}).(\color{green}{q}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{9}{13})} . \color{green}{(q)} + \color{orange}{(\frac{9}{13})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{10}p+\frac{9}{13}q+\frac{9}{13}.\frac{7}{10}& \text{Uitwerken } \\ & =pq+\frac{7}{10}p+\frac{9}{13}q+\frac{63}{130} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)