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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{4}{17})(\frac{4}{2}+q)& =(\color{red}{a}+\color{orange}{\frac{4}{17}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{4}{17})} . \color{green}{(q)} + \color{orange}{(\frac{4}{17})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2a+\frac{4}{17}q+\frac{4}{17}.2& \text{Uitwerken } \\ & =aq+2a+\frac{4}{17}q+\frac{8}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{1}{2})(\frac{-16}{9}-b)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-b}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{16}{9}q+\frac{1}{2}b+\frac{1}{2}.\frac{16}{9}& \text{Uitwerken } \\ & =-bq-\frac{16}{9}q+\frac{1}{2}b+\frac{16}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{16}{9}q+\frac{1}{2}b+\frac{8}{9} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-10}{18}+a)(p-\frac{2}{9})& =(\color{red}{a}+\color{orange}{\frac{-5}{9}}).(\color{green}{p}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{9}a-\frac{5}{9}p+\frac{5}{9}.\frac{2}{9}& \text{Uitwerken } \\ & =ap-\frac{2}{9}a-\frac{5}{9}p+\frac{10}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-(-2))(q-\frac{-12}{4})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qq+3q+2q+2.3& \text{Uitwerken } \\ & =q^2+(3+2)q+6 & \text{Neem samen} \\ &=q^2+5q+6 & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(b-\frac{10}{2})(a-\frac{15}{17})& =(\color{red}{b}+\color{orange}{(-5)}).(\color{green}{a}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(-5)} . \color{green}{(a)} + \color{orange}{(-5)} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{17}b-5a+5.\frac{15}{17}& \text{Uitwerken } \\ & =ab-\frac{15}{17}b-5a+\frac{75}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{3}{13})(q-\frac{-2}{10})& =(\color{red}{b}+\color{orange}{\frac{3}{13}}).(\color{green}{q}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{3}{13})} . \color{green}{(q)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{5}b+\frac{3}{13}q+\frac{3}{13}.\frac{1}{5}& \text{Uitwerken } \\ & =bq+\frac{1}{5}b+\frac{3}{13}q+\frac{3}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{-18}{5})(\frac{3}{10}+p)& =(\color{red}{q}+\color{orange}{\frac{-18}{5}}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{10}q-\frac{18}{5}p-\frac{18}{5}.\frac{3}{10}& \text{Uitwerken } \\ & =pq+\frac{3}{10}q-\frac{18}{5}p-\frac{54}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{3}{10}q-\frac{18}{5}p-\frac{27}{25} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(b+\frac{17}{7})(p+\frac{-4}{20})& =(\color{red}{b}+\color{orange}{\frac{17}{7}}).(\color{green}{p}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{17}{7})} . \color{green}{(p)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{5}b+\frac{17}{7}p-\frac{17}{7}.\frac{1}{5}& \text{Uitwerken } \\ & =bp-\frac{1}{5}b+\frac{17}{7}p-\frac{17}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q+\frac{12}{9})(p-\frac{-11}{17})& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{17}q+\frac{4}{3}p+\frac{4}{3}.\frac{11}{17}& \text{Uitwerken } \\ & =pq+\frac{11}{17}q+\frac{4}{3}p+\frac{44}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-14}{11}-x)(q+\frac{16}{10})& =(\color{red}{-x}+\color{orange}{\frac{-14}{11}}).(\color{green}{q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{8}{5}x-\frac{14}{11}q-\frac{14}{11}.\frac{8}{5}& \text{Uitwerken } \\ & =-qx-\frac{8}{5}x-\frac{14}{11}q-\frac{112}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q+\frac{-8}{4})(p-\frac{14}{4})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{2}q-2p+2.\frac{7}{2}& \text{Uitwerken } \\ & =pq-\frac{7}{2}q-2p+\frac{14}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{7}{2}q-2p+7 & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-8}{15}+x)(b-\frac{-7}{15})& =(\color{red}{x}+\color{orange}{\frac{-8}{15}}).(\color{green}{b}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{15}x-\frac{8}{15}b-\frac{8}{15}.\frac{7}{15}& \text{Uitwerken } \\ & =bx+\frac{7}{15}x-\frac{8}{15}b-\frac{56}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)