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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-7}{10}-q)(p-\frac{-3}{18})& =(\color{red}{-q}+\color{orange}{\frac{-7}{10}}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{6}q-\frac{7}{10}p-\frac{7}{10}.\frac{1}{6}& \text{Uitwerken } \\ & =-pq-\frac{1}{6}q-\frac{7}{10}p-\frac{7}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}((-3)+a)(q+\frac{4}{12})& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(-3)} . \color{green}{(q)} + \color{orange}{(-3)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{3}a-3q-3.\frac{1}{3}& \text{Uitwerken } \\ & =aq+\frac{1}{3}a-3q-\frac{3}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{1}{3}a-3q-1 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(a+\frac{-2}{16})(9-a)& =(\color{red}{a}+\color{orange}{\frac{-1}{8}}).(\color{green}{-a}+\color{blue}{9})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(9)} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = -aa+9a+\frac{1}{8}a-\frac{1}{8}.9& \text{Uitwerken } \\ & =-a^2+(9+\frac{1}{8})a-\frac{9}{8} & \text{Neem samen} \\ &=-a^2+\frac{73}{8}a-\frac{9}{8} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(a+\frac{11}{6})(\frac{-7}{12}+b)& =(\color{red}{a}+\color{orange}{\frac{11}{6}}).(\color{green}{b}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{11}{6})} . \color{green}{(b)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{12}a+\frac{11}{6}b-\frac{11}{6}.\frac{7}{12}& \text{Uitwerken } \\ & =ab-\frac{7}{12}a+\frac{11}{6}b-\frac{77}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q+\frac{13}{19})(p-\frac{-16}{17})& =(\color{red}{q}+\color{orange}{\frac{13}{19}}).(\color{green}{p}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{13}{19})} . \color{green}{(p)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{16}{17}q+\frac{13}{19}p+\frac{13}{19}.\frac{16}{17}& \text{Uitwerken } \\ & =pq+\frac{16}{17}q+\frac{13}{19}p+\frac{208}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{13}{8}+a)(q+\frac{8}{8})& =(\color{red}{a}+\color{orange}{\frac{13}{8}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{13}{8})} . \color{green}{(q)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq+1a+\frac{13}{8}q+\frac{13}{8}.1& \text{Uitwerken } \\ & =aq+1a+\frac{13}{8}q+\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{8}{5})(b-\frac{-2}{2})& =(\color{red}{a}+\color{orange}{\frac{-8}{5}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-8}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1a-\frac{8}{5}b-\frac{8}{5}.1& \text{Uitwerken } \\ & =ab+1a-\frac{8}{5}b-\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{-20}{7})(\frac{14}{4}-x)& =(\color{red}{p}+\color{orange}{\frac{-20}{7}}).(\color{green}{-x}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{2}p+\frac{20}{7}x-\frac{20}{7}.\frac{7}{2}& \text{Uitwerken } \\ & =-px+\frac{7}{2}p+\frac{20}{7}x-\frac{140}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{7}{2}p+\frac{20}{7}x-10 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q+\frac{5}{18})(q+\frac{7}{2})& =(\color{red}{q}+\color{orange}{\frac{5}{18}}).(\color{green}{q}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{5}{18})} . \color{green}{(q)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{2}q+\frac{5}{18}q+\frac{5}{18}.\frac{7}{2}& \text{Uitwerken } \\ & =q^2+(\frac{7}{2}+\frac{5}{18})q+\frac{35}{36} & \text{Neem samen} \\ &=q^2+\frac{68}{18}q+\frac{35}{36} & \text{Maak de som} \\ &=q^2+\frac{34}{9}q+\frac{35}{36} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(\frac{10}{15}-x)(q+\frac{-17}{15})& =(\color{red}{-x}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{17}{15}x+\frac{2}{3}q-\frac{2}{3}.\frac{17}{15}& \text{Uitwerken } \\ & =-qx+\frac{17}{15}x+\frac{2}{3}q-\frac{34}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{9}{10})(q+\frac{-4}{3})& =(\color{red}{a}+\color{orange}{\frac{9}{10}}).(\color{green}{q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{9}{10})} . \color{green}{(q)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{3}a+\frac{9}{10}q-\frac{9}{10}.\frac{4}{3}& \text{Uitwerken } \\ & =aq-\frac{4}{3}a+\frac{9}{10}q-\frac{36}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{4}{3}a+\frac{9}{10}q-\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(a-\frac{9}{9})(\frac{-14}{12}+q)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{6}a-1q+1.\frac{7}{6}& \text{Uitwerken } \\ & =aq-\frac{7}{6}a-1q+\frac{7}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)