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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-13}{3}-a)(\frac{11}{6}+x)& =(\color{red}{-a}+\color{orange}{\frac{-13}{3}}).(\color{green}{x}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{6}a-\frac{13}{3}x-\frac{13}{3}.\frac{11}{6}& \text{Uitwerken } \\ & =-ax-\frac{11}{6}a-\frac{13}{3}x-\frac{143}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-\frac{16}{8})(\frac{-7}{17}+a)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{17}x-2a+2.\frac{7}{17}& \text{Uitwerken } \\ & =ax-\frac{7}{17}x-2a+\frac{14}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-5}{4}+a)(b+\frac{-16}{12})& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{3}a-\frac{5}{4}b+\frac{5}{4}.\frac{4}{3}& \text{Uitwerken } \\ & =ab-\frac{4}{3}a-\frac{5}{4}b+\frac{20}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{4}{3}a-\frac{5}{4}b+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(q+\frac{-5}{15})(\frac{12}{12}+p)& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1q-\frac{1}{3}p-\frac{1}{3}.1& \text{Uitwerken } \\ & =pq+1q-\frac{1}{3}p-\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q-\frac{17}{10})(\frac{5}{13}-q)& =(\color{red}{q}+\color{orange}{\frac{-17}{10}}).(\color{green}{-q}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{5}{13}q+\frac{17}{10}q-\frac{17}{10}.\frac{5}{13}& \text{Uitwerken } \\ & =-q^2+(\frac{5}{13}+\frac{17}{10})q-\frac{85}{130} & \text{Neem samen} \\ &=-q^2+\frac{271}{130}q-\frac{85}{130} & \text{Maak de som} \\ &=-q^2+\frac{271}{130}q-\frac{17}{26} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
6. \(\begin{align}(\frac{15}{14}-q)(x-\frac{6}{16})& =(\color{red}{-q}+\color{orange}{\frac{15}{14}}).(\color{green}{x}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{15}{14})} . \color{green}{(x)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{8}q+\frac{15}{14}x-\frac{15}{14}.\frac{3}{8}& \text{Uitwerken } \\ & =-qx+\frac{3}{8}q+\frac{15}{14}x-\frac{45}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{-10}{11})(\frac{-16}{19}-p)& =(\color{red}{a}+\color{orange}{\frac{10}{11}}).(\color{green}{-p}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{10}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{16}{19}a-\frac{10}{11}p-\frac{10}{11}.\frac{16}{19}& \text{Uitwerken } \\ & =-ap-\frac{16}{19}a-\frac{10}{11}p-\frac{160}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-12}{13}+x)(p+\frac{7}{7})& =(\color{red}{x}+\color{orange}{\frac{-12}{13}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-12}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1x-\frac{12}{13}p-\frac{12}{13}.1& \text{Uitwerken } \\ & =px+1x-\frac{12}{13}p-\frac{12}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{18}{3}+x)(p-\frac{-14}{15})& =(\color{red}{x}+\color{orange}{6}).(\color{green}{p}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{14}{15}x+6p+6.\frac{14}{15}& \text{Uitwerken } \\ & =px+\frac{14}{15}x+6p+\frac{84}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{14}{15}x+6p+\frac{28}{5} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p+\frac{-13}{4})(q+\frac{8}{9})& =(\color{red}{p}+\color{orange}{\frac{-13}{4}}).(\color{green}{q}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{9}p-\frac{13}{4}q-\frac{13}{4}.\frac{8}{9}& \text{Uitwerken } \\ & =pq+\frac{8}{9}p-\frac{13}{4}q-\frac{104}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{8}{9}p-\frac{13}{4}q-\frac{26}{9} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(a-\frac{5}{11})(\frac{11}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{-5}{11}}).(\color{green}{q}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{17}a-\frac{5}{11}q-\frac{5}{11}.\frac{11}{17}& \text{Uitwerken } \\ & =aq+\frac{11}{17}a-\frac{5}{11}q-\frac{55}{187} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{11}{17}a-\frac{5}{11}q-\frac{5}{17} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x+\frac{-16}{14})(a-\frac{1}{11})& =(\color{red}{x}+\color{orange}{\frac{-8}{7}}).(\color{green}{a}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{11}x-\frac{8}{7}a+\frac{8}{7}.\frac{1}{11}& \text{Uitwerken } \\ & =ax-\frac{1}{11}x-\frac{8}{7}a+\frac{8}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)