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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{18}{8}+a)(b+\frac{17}{4})& =(\color{red}{a}+\color{orange}{\frac{9}{4}}).(\color{green}{b}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{9}{4})} . \color{green}{(b)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{4}a+\frac{9}{4}b+\frac{9}{4}.\frac{17}{4}& \text{Uitwerken } \\ & =ab+\frac{17}{4}a+\frac{9}{4}b+\frac{153}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-\frac{3}{15})(q-\frac{-1}{3})& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{3}x-\frac{1}{5}q-\frac{1}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =qx+\frac{1}{3}x-\frac{1}{5}q-\frac{1}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{10}{18})(q-\frac{17}{14})& =(\color{red}{p}+\color{orange}{\frac{-5}{9}}).(\color{green}{q}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{14}p-\frac{5}{9}q+\frac{5}{9}.\frac{17}{14}& \text{Uitwerken } \\ & =pq-\frac{17}{14}p-\frac{5}{9}q+\frac{85}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{14}{16}-a)(q+\frac{-18}{13})& =(\color{red}{-a}+\color{orange}{\frac{7}{8}}).(\color{green}{q}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{18}{13}a+\frac{7}{8}q-\frac{7}{8}.\frac{18}{13}& \text{Uitwerken } \\ & =-aq+\frac{18}{13}a+\frac{7}{8}q-\frac{126}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{18}{13}a+\frac{7}{8}q-\frac{63}{52} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-18}{6}-a)(\frac{15}{8}-p)& =(\color{red}{-a}+\color{orange}{(-3)}).(\color{green}{-p}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(-3)} . \color{green}{(-p)} + \color{orange}{(-3)} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{8}a+3p-3.\frac{15}{8}& \text{Uitwerken } \\ & =ap-\frac{15}{8}a+3p-\frac{45}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-18}{13}+x)(x-\frac{-16}{11})& =(\color{red}{x}+\color{orange}{\frac{-18}{13}}).(\color{green}{x}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{-18}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{16}{11}x-\frac{18}{13}x-\frac{18}{13}.\frac{16}{11}& \text{Uitwerken } \\ & =x^2+(\frac{16}{11}+(\frac{-18}{13}))x-(\frac{-288}{143}) & \text{Neem samen} \\ &=x^2+\frac{10}{143}x-(\frac{-288}{143}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{-17}{14}-x)(q+\frac{-7}{7})& =(\color{red}{-x}+\color{orange}{\frac{-17}{14}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-17}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1x-\frac{17}{14}q+\frac{17}{14}.1& \text{Uitwerken } \\ & =-qx+1x-\frac{17}{14}q+\frac{17}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{18}{9})(q+\frac{-17}{3})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{3}p-2q+2.\frac{17}{3}& \text{Uitwerken } \\ & =pq-\frac{17}{3}p-2q+\frac{34}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{13}{4}+b)(\frac{5}{8}-q)& =(\color{red}{b}+\color{orange}{\frac{13}{4}}).(\color{green}{-q}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{13}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{8}b-\frac{13}{4}q+\frac{13}{4}.\frac{5}{8}& \text{Uitwerken } \\ & =-bq+\frac{5}{8}b-\frac{13}{4}q+\frac{65}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-5}{15})(b-\frac{-15}{7})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{7}x+\frac{1}{3}b+\frac{1}{3}.\frac{15}{7}& \text{Uitwerken } \\ & =bx+\frac{15}{7}x+\frac{1}{3}b+\frac{15}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{7}x+\frac{1}{3}b+\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-3}{3}+q)(\frac{1}{14}+b)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{14}q-1b-1.\frac{1}{14}& \text{Uitwerken } \\ & =bq+\frac{1}{14}q-1b-\frac{1}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a+\frac{-6}{17})(\frac{12}{15}-a)& =(\color{red}{a}+\color{orange}{\frac{-6}{17}}).(\color{green}{-a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{4}{5}a+\frac{6}{17}a-\frac{6}{17}.\frac{4}{5}& \text{Uitwerken } \\ & =-a^2+(\frac{4}{5}+\frac{6}{17})a-\frac{24}{85} & \text{Neem samen} \\ &=-a^2+\frac{98}{85}a-\frac{24}{85} & \text{Maak de som} \\\end{align}\)