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

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Werk uit en vereenvoudig

1. \((\frac{-15}{20}-x)(\frac{6}{13}+a)\)
2. \((\frac{7}{9}-p)(x-\frac{6}{3})\)
3. \((x-19)(\frac{-5}{5}+q)\)
4. \((a-\frac{12}{17})(\frac{13}{3}-x)\)
5. \((\frac{20}{13}-b)(\frac{15}{20}-x)\)
6. \((\frac{-14}{17}-b)((-18)-q)\)
7. \((\frac{1}{11}+q)(p+\frac{-4}{16})\)
8. \((x+\frac{-7}{11})(b+\frac{8}{7})\)
9. \((a+\frac{4}{9})(q+\frac{-3}{2})\)
10. \((q+\frac{-9}{3})(\frac{-18}{20}+b)\)
11. \((\frac{1}{6}+b)(x-\frac{-5}{14})\)
12. \((b+\frac{-9}{8})(x-\frac{2}{18})\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-15}{20}-x)(\frac{6}{13}+a)& =(\color{red}{-x}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{6}{13}x-\frac{3}{4}a-\frac{3}{4}.\frac{6}{13}& \text{Uitwerken } \\ & =-ax-\frac{6}{13}x-\frac{3}{4}a-\frac{18}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{6}{13}x-\frac{3}{4}a-\frac{9}{26} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{7}{9}-p)(x-\frac{6}{3})& =(\color{red}{-p}+\color{orange}{\frac{7}{9}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(\frac{7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -px+2p+\frac{7}{9}x-\frac{7}{9}.2& \text{Uitwerken } \\ & =-px+2p+\frac{7}{9}x-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-19)(\frac{-5}{5}+q)& =(\color{red}{x}+\color{orange}{(-19)}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(-19)} . \color{green}{(q)} + \color{orange}{(-19)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1x-19q+19.1& \text{Uitwerken } \\ & =qx-1x-19q+19 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{12}{17})(\frac{13}{3}-x)& =(\color{red}{a}+\color{orange}{\frac{-12}{17}}).(\color{green}{-x}+\color{blue}{\frac{13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{13}{3})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{13}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{3}a+\frac{12}{17}x-\frac{12}{17}.\frac{13}{3}& \text{Uitwerken } \\ & =-ax+\frac{13}{3}a+\frac{12}{17}x-\frac{156}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{13}{3}a+\frac{12}{17}x-\frac{52}{17} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{20}{13}-b)(\frac{15}{20}-x)& =(\color{red}{-b}+\color{orange}{\frac{20}{13}}).(\color{green}{-x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{20}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{4}b-\frac{20}{13}x+\frac{20}{13}.\frac{3}{4}& \text{Uitwerken } \\ & =bx-\frac{3}{4}b-\frac{20}{13}x+\frac{60}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{3}{4}b-\frac{20}{13}x+\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-14}{17}-b)((-18)-q)& =(\color{red}{-b}+\color{orange}{\frac{-14}{17}}).(\color{green}{-q}+\color{blue}{(-18)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(-18)} + \color{orange}{(\frac{-14}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = bq+18b+\frac{14}{17}q+\frac{14}{17}.18& \text{Uitwerken } \\ & =bq+18b+\frac{14}{17}q+\frac{252}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{1}{11}+q)(p+\frac{-4}{16})& =(\color{red}{q}+\color{orange}{\frac{1}{11}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{1}{11})} . \color{green}{(p)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{4}q+\frac{1}{11}p-\frac{1}{11}.\frac{1}{4}& \text{Uitwerken } \\ & =pq-\frac{1}{4}q+\frac{1}{11}p-\frac{1}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x+\frac{-7}{11})(b+\frac{8}{7})& =(\color{red}{x}+\color{orange}{\frac{-7}{11}}).(\color{green}{b}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{7}x-\frac{7}{11}b-\frac{7}{11}.\frac{8}{7}& \text{Uitwerken } \\ & =bx+\frac{8}{7}x-\frac{7}{11}b-\frac{56}{77} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{8}{7}x-\frac{7}{11}b-\frac{8}{11} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a+\frac{4}{9})(q+\frac{-3}{2})& =(\color{red}{a}+\color{orange}{\frac{4}{9}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{2}a+\frac{4}{9}q-\frac{4}{9}.\frac{3}{2}& \text{Uitwerken } \\ & =aq-\frac{3}{2}a+\frac{4}{9}q-\frac{12}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{3}{2}a+\frac{4}{9}q-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q+\frac{-9}{3})(\frac{-18}{20}+b)& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{10}q-3b+3.\frac{9}{10}& \text{Uitwerken } \\ & =bq-\frac{9}{10}q-3b+\frac{27}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{1}{6}+b)(x-\frac{-5}{14})& =(\color{red}{b}+\color{orange}{\frac{1}{6}}).(\color{green}{x}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{14}b+\frac{1}{6}x+\frac{1}{6}.\frac{5}{14}& \text{Uitwerken } \\ & =bx+\frac{5}{14}b+\frac{1}{6}x+\frac{5}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{-9}{8})(x-\frac{2}{18})& =(\color{red}{b}+\color{orange}{\frac{-9}{8}}).(\color{green}{x}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{9}b-\frac{9}{8}x+\frac{9}{8}.\frac{1}{9}& \text{Uitwerken } \\ & =bx-\frac{1}{9}b-\frac{9}{8}x+\frac{9}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{9}b-\frac{9}{8}x+\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)