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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{12}{12}-p)(\frac{-8}{3}+x)& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{8}{3}p+1x-1.\frac{8}{3}& \text{Uitwerken } \\ & =-px+\frac{8}{3}p+1x-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-1}{15}+b)(a+\frac{6}{5})& =(\color{red}{b}+\color{orange}{\frac{-1}{15}}).(\color{green}{a}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{6}{5}b-\frac{1}{15}a-\frac{1}{15}.\frac{6}{5}& \text{Uitwerken } \\ & =ab+\frac{6}{5}b-\frac{1}{15}a-\frac{6}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{6}{5}b-\frac{1}{15}a-\frac{2}{25} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(a-\frac{3}{4})(q-\frac{-19}{14})& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{14}a-\frac{3}{4}q-\frac{3}{4}.\frac{19}{14}& \text{Uitwerken } \\ & =aq+\frac{19}{14}a-\frac{3}{4}q-\frac{57}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-20}{12}+x)(p-\frac{-14}{4})& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{p}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{2}x-\frac{5}{3}p-\frac{5}{3}.\frac{7}{2}& \text{Uitwerken } \\ & =px+\frac{7}{2}x-\frac{5}{3}p-\frac{35}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a+\frac{-19}{16})(\frac{-19}{6}-a)& =(\color{red}{a}+\color{orange}{\frac{-19}{16}}).(\color{green}{-a}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{19}{6}a+\frac{19}{16}a+\frac{19}{16}.\frac{19}{6}& \text{Uitwerken } \\ & =-a^2+((\frac{-19}{6})+\frac{19}{16})a+(\frac{-361}{96}) & \text{Neem samen} \\ &=-a^2-\frac{95}{48}a+(\frac{-361}{96}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{12}{9}-a)(\frac{3}{10}-b)& =(\color{red}{-a}+\color{orange}{\frac{4}{3}}).(\color{green}{-b}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{10}a-\frac{4}{3}b+\frac{4}{3}.\frac{3}{10}& \text{Uitwerken } \\ & =ab-\frac{3}{10}a-\frac{4}{3}b+\frac{12}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{3}{10}a-\frac{4}{3}b+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{17}{16}-q)(a-\frac{10}{2})& =(\color{red}{-q}+\color{orange}{\frac{17}{16}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-5)} + \color{orange}{(\frac{17}{16})} . \color{green}{(a)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -aq+5q+\frac{17}{16}a-\frac{17}{16}.5& \text{Uitwerken } \\ & =-aq+5q+\frac{17}{16}a-\frac{85}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q+\frac{-8}{17})(b+\frac{6}{19})& =(\color{red}{q}+\color{orange}{\frac{-8}{17}}).(\color{green}{b}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{6}{19}q-\frac{8}{17}b-\frac{8}{17}.\frac{6}{19}& \text{Uitwerken } \\ & =bq+\frac{6}{19}q-\frac{8}{17}b-\frac{48}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{3}{20}+a)(\frac{-17}{13}-q)& =(\color{red}{a}+\color{orange}{\frac{3}{20}}).(\color{green}{-q}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{3}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{17}{13}a-\frac{3}{20}q-\frac{3}{20}.\frac{17}{13}& \text{Uitwerken } \\ & =-aq-\frac{17}{13}a-\frac{3}{20}q-\frac{51}{260} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-5}{4}-x)(\frac{9}{16}-p)& =(\color{red}{-x}+\color{orange}{\frac{-5}{4}}).(\color{green}{-p}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{16}x+\frac{5}{4}p-\frac{5}{4}.\frac{9}{16}& \text{Uitwerken } \\ & =px-\frac{9}{16}x+\frac{5}{4}p-\frac{45}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{7}{9}-a)(\frac{-8}{7}+q)& =(\color{red}{-a}+\color{orange}{\frac{7}{9}}).(\color{green}{q}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{8}{7}a+\frac{7}{9}q-\frac{7}{9}.\frac{8}{7}& \text{Uitwerken } \\ & =-aq+\frac{8}{7}a+\frac{7}{9}q-\frac{56}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{8}{7}a+\frac{7}{9}q-\frac{8}{9} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-20}{2}-x)(x-\frac{15}{9})& =(\color{red}{-x}+\color{orange}{(-10)}).(\color{green}{x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(-10)} . \color{green}{(x)} + \color{orange}{(-10)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{5}{3}x-10x+10.\frac{5}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{5}{3}+(-10))x+(\frac{-50}{3}) & \text{Neem samen} \\ &=-x^2-\frac{25}{3}x+(\frac{-50}{3}) & \text{Maak de som} \\\end{align}\)