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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-5}{2}-p)(\frac{-9}{8}+p)& =(\color{red}{-p}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{9}{8}p-\frac{5}{2}p+\frac{5}{2}.\frac{9}{8}& \text{Uitwerken } \\ & =-p^2+(\frac{9}{8}+(\frac{-5}{2}))p+(\frac{-45}{16}) & \text{Neem samen} \\ &=-p^2-\frac{11}{8}p+(\frac{-45}{16}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(p-\frac{-4}{4})(\frac{-1}{14}-q)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{14}p-1q-1.\frac{1}{14}& \text{Uitwerken } \\ & =-pq-\frac{1}{14}p-1q-\frac{1}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{9}{9})(\frac{4}{15}-x)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{4}{15}q+1x-1.\frac{4}{15}& \text{Uitwerken } \\ & =-qx+\frac{4}{15}q+1x-\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q+\frac{-18}{17})(p-\frac{12}{3})& =(\color{red}{q}+\color{orange}{\frac{-18}{17}}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(\frac{-18}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = pq-4q-\frac{18}{17}p+\frac{18}{17}.4& \text{Uitwerken } \\ & =pq-4q-\frac{18}{17}p+\frac{72}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-7}{3}+a)(q-\frac{-3}{13})& =(\color{red}{a}+\color{orange}{\frac{-7}{3}}).(\color{green}{q}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{13}a-\frac{7}{3}q-\frac{7}{3}.\frac{3}{13}& \text{Uitwerken } \\ & =aq+\frac{3}{13}a-\frac{7}{3}q-\frac{21}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{13}a-\frac{7}{3}q-\frac{7}{13} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b+\frac{5}{10})(\frac{8}{2}+q)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(4)} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bq+4b+\frac{1}{2}q+\frac{1}{2}.4& \text{Uitwerken } \\ & =bq+4b+\frac{1}{2}q+\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+4b+\frac{1}{2}q+2 & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-9}{20}+a)(\frac{11}{8}-p)& =(\color{red}{a}+\color{orange}{\frac{-9}{20}}).(\color{green}{-p}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{11}{8}a+\frac{9}{20}p-\frac{9}{20}.\frac{11}{8}& \text{Uitwerken } \\ & =-ap+\frac{11}{8}a+\frac{9}{20}p-\frac{99}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-9}{3}-x)(b+\frac{-17}{20})& =(\color{red}{-x}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{17}{20}x-3b+3.\frac{17}{20}& \text{Uitwerken } \\ & =-bx+\frac{17}{20}x-3b+\frac{51}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{16}{3})(a-\frac{-14}{7})& =(\color{red}{x}+\color{orange}{\frac{16}{3}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{16}{3})} . \color{green}{(a)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2x+\frac{16}{3}a+\frac{16}{3}.2& \text{Uitwerken } \\ & =ax+2x+\frac{16}{3}a+\frac{32}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b+\frac{-19}{9})(q-\frac{-17}{9})& =(\color{red}{b}+\color{orange}{\frac{-19}{9}}).(\color{green}{q}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{9}b-\frac{19}{9}q-\frac{19}{9}.\frac{17}{9}& \text{Uitwerken } \\ & =bq+\frac{17}{9}b-\frac{19}{9}q-\frac{323}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q+\frac{20}{15})(\frac{15}{4}-a)& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{-a}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{15}{4}q-\frac{4}{3}a+\frac{4}{3}.\frac{15}{4}& \text{Uitwerken } \\ & =-aq+\frac{15}{4}q-\frac{4}{3}a+\frac{60}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{15}{4}q-\frac{4}{3}a+5 & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q-\frac{-17}{17})(\frac{15}{11}+a)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{15}{11}q+1a+1.\frac{15}{11}& \text{Uitwerken } \\ & =aq+\frac{15}{11}q+1a+\frac{15}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)