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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{-7}{10})(\frac{-8}{16}+b)& =(\color{red}{q}+\color{orange}{\frac{-7}{10}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{2}q-\frac{7}{10}b+\frac{7}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =bq-\frac{1}{2}q-\frac{7}{10}b+\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{-11}{9})(\frac{4}{3}+q)& =(\color{red}{a}+\color{orange}{\frac{-11}{9}}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{3}a-\frac{11}{9}q-\frac{11}{9}.\frac{4}{3}& \text{Uitwerken } \\ & =aq+\frac{4}{3}a-\frac{11}{9}q-\frac{44}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{-20}{2})(q-\frac{-15}{15})& =(\color{red}{p}+\color{orange}{10}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(10)} . \color{green}{(q)} + \color{orange}{(10)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p+10q+10.1& \text{Uitwerken } \\ & =pq+1p+10q+10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{16}{8}+a)(p-\frac{19}{16})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{16}a+2p-2.\frac{19}{16}& \text{Uitwerken } \\ & =ap-\frac{19}{16}a+2p-\frac{38}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{19}{16}a+2p-\frac{19}{8} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(q+\frac{15}{13})(\frac{18}{7}+q)& =(\color{red}{q}+\color{orange}{\frac{15}{13}}).(\color{green}{q}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{15}{13})} . \color{green}{(q)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{18}{7}q+\frac{15}{13}q+\frac{15}{13}.\frac{18}{7}& \text{Uitwerken } \\ & =q^2+(\frac{18}{7}+\frac{15}{13})q+\frac{270}{91} & \text{Neem samen} \\ &=q^2+\frac{339}{91}q+\frac{270}{91} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(x-\frac{-7}{13})(q-\frac{-18}{12})& =(\color{red}{x}+\color{orange}{\frac{7}{13}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{7}{13})} . \color{green}{(q)} + \color{orange}{(\frac{7}{13})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{2}x+\frac{7}{13}q+\frac{7}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =qx+\frac{3}{2}x+\frac{7}{13}q+\frac{21}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{-1}{11})(\frac{-11}{8}-q)& =(\color{red}{x}+\color{orange}{\frac{-1}{11}}).(\color{green}{-q}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{11}{8}x+\frac{1}{11}q+\frac{1}{11}.\frac{11}{8}& \text{Uitwerken } \\ & =-qx-\frac{11}{8}x+\frac{1}{11}q+\frac{11}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{11}{8}x+\frac{1}{11}q+\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(b+\frac{4}{12})(\frac{-3}{4}+b)& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{4}b+\frac{1}{3}b-\frac{1}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{4})+\frac{1}{3})b-(\frac{-3}{12}) & \text{Neem samen} \\ &=b^2-\frac{5}{12}b-(\frac{-3}{12}) & \text{Maak de som} \\ &=b^2-\frac{5}{12}b+\frac{1}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
9. \(\begin{align}(\frac{-10}{3}+b)(q+\frac{-14}{17})& =(\color{red}{b}+\color{orange}{\frac{-10}{3}}).(\color{green}{q}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{14}{17}b-\frac{10}{3}q+\frac{10}{3}.\frac{14}{17}& \text{Uitwerken } \\ & =bq-\frac{14}{17}b-\frac{10}{3}q+\frac{140}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{19}{8}-b)(\frac{14}{20}+x)& =(\color{red}{-b}+\color{orange}{\frac{19}{8}}).(\color{green}{x}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{19}{8})} . \color{green}{(x)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{7}{10}b+\frac{19}{8}x+\frac{19}{8}.\frac{7}{10}& \text{Uitwerken } \\ & =-bx-\frac{7}{10}b+\frac{19}{8}x+\frac{133}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-\frac{-12}{11})(a+\frac{15}{11})& =(\color{red}{x}+\color{orange}{\frac{12}{11}}).(\color{green}{a}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{12}{11})} . \color{green}{(a)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{15}{11}x+\frac{12}{11}a+\frac{12}{11}.\frac{15}{11}& \text{Uitwerken } \\ & =ax+\frac{15}{11}x+\frac{12}{11}a+\frac{180}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-9}{9}+q)(q-\frac{15}{8})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{15}{8}q-1q+1.\frac{15}{8}& \text{Uitwerken } \\ & =q^2+((\frac{-15}{8})+(-1))q+\frac{15}{8} & \text{Neem samen} \\ &=q^2-\frac{23}{8}q+\frac{15}{8} & \text{Maak de som} \\\end{align}\)