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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{13}{9})(\frac{9}{7}-p)& =(\color{red}{q}+\color{orange}{\frac{13}{9}}).(\color{green}{-p}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{13}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{7}q-\frac{13}{9}p+\frac{13}{9}.\frac{9}{7}& \text{Uitwerken } \\ & =-pq+\frac{9}{7}q-\frac{13}{9}p+\frac{117}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{9}{7}q-\frac{13}{9}p+\frac{13}{7} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-18}{18}+x)(\frac{-3}{19}+b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{19}x-1b+1.\frac{3}{19}& \text{Uitwerken } \\ & =bx-\frac{3}{19}x-1b+\frac{3}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}((-14)+q)(\frac{11}{13}-b)& =(\color{red}{q}+\color{orange}{(-14)}).(\color{green}{-b}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(-14)} . \color{green}{(-b)} + \color{orange}{(-14)} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{11}{13}q+14b-14.\frac{11}{13}& \text{Uitwerken } \\ & =-bq+\frac{11}{13}q+14b-\frac{154}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-\frac{-18}{17})(x-\frac{-9}{10})& =(\color{red}{b}+\color{orange}{\frac{18}{17}}).(\color{green}{x}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{18}{17})} . \color{green}{(x)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{10}b+\frac{18}{17}x+\frac{18}{17}.\frac{9}{10}& \text{Uitwerken } \\ & =bx+\frac{9}{10}b+\frac{18}{17}x+\frac{162}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{9}{10}b+\frac{18}{17}x+\frac{81}{85} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-9}{3}+a)(\frac{-16}{2}+x)& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{(-8)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-8)} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = ax-8a-3x+3.8& \text{Uitwerken } \\ & =ax-8a-3x+24 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{8}{2})(\frac{-16}{16}+b)& =(\color{red}{b}+\color{orange}{4}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(4)} . \color{green}{(b)} + \color{orange}{(4)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bb-1b+4b-4.1& \text{Uitwerken } \\ & =b^2+((-1)+4)b-(-4) & \text{Neem samen} \\ &=b^2+3b-(-4) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(p-\frac{-14}{6})(x-\frac{18}{18})& =(\color{red}{p}+\color{orange}{\frac{7}{3}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{3})} . \color{green}{(x)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p+\frac{7}{3}x-\frac{7}{3}.1& \text{Uitwerken } \\ & =px-1p+\frac{7}{3}x-\frac{7}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x+\frac{14}{13})(\frac{-15}{18}-p)& =(\color{red}{x}+\color{orange}{\frac{14}{13}}).(\color{green}{-p}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{14}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{5}{6}x-\frac{14}{13}p-\frac{14}{13}.\frac{5}{6}& \text{Uitwerken } \\ & =-px-\frac{5}{6}x-\frac{14}{13}p-\frac{70}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{5}{6}x-\frac{14}{13}p-\frac{35}{39} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a+\frac{-3}{15})(q+\frac{9}{11})& =(\color{red}{a}+\color{orange}{\frac{-1}{5}}).(\color{green}{q}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{11}a-\frac{1}{5}q-\frac{1}{5}.\frac{9}{11}& \text{Uitwerken } \\ & =aq+\frac{9}{11}a-\frac{1}{5}q-\frac{9}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p+\frac{15}{10})(\frac{-12}{5}-p)& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{-p}+\color{blue}{\frac{-12}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-12}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{12}{5}p-\frac{3}{2}p-\frac{3}{2}.\frac{12}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-12}{5})+(\frac{-3}{2}))p-\frac{36}{10} & \text{Neem samen} \\ &=-p^2-\frac{39}{10}p-\frac{36}{10} & \text{Maak de som} \\ &=-p^2-\frac{39}{10}p-\frac{18}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(p+\frac{-7}{2})(\frac{3}{15}-x)& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{-x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{5}p+\frac{7}{2}x-\frac{7}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =-px+\frac{1}{5}p+\frac{7}{2}x-\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{9}{3})(q+\frac{-9}{15})& =(\color{red}{p}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{5}p+3q-3.\frac{3}{5}& \text{Uitwerken } \\ & =pq-\frac{3}{5}p+3q-\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)