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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-15}{13}-b)(q-\frac{-14}{5})& =(\color{red}{-b}+\color{orange}{\frac{-15}{13}}).(\color{green}{q}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{14}{5}b-\frac{15}{13}q-\frac{15}{13}.\frac{14}{5}& \text{Uitwerken } \\ & =-bq-\frac{14}{5}b-\frac{15}{13}q-\frac{210}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{14}{5}b-\frac{15}{13}q-\frac{42}{13} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-8}{12}-x)(x-\frac{7}{10})& =(\color{red}{-x}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{7}{10}x-\frac{2}{3}x+\frac{2}{3}.\frac{7}{10}& \text{Uitwerken } \\ & =-x^2+(\frac{7}{10}+(\frac{-2}{3}))x+(\frac{-14}{30}) & \text{Neem samen} \\ &=-x^2+\frac{1}{30}x+(\frac{-14}{30}) & \text{Maak de som} \\ &=-x^2+\frac{1}{30}x+(\frac{-7}{15}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
3. \(\begin{align}(\frac{20}{20}-x)(\frac{-8}{15}-b)& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{15}x-1b-1.\frac{8}{15}& \text{Uitwerken } \\ & =bx+\frac{8}{15}x-1b-\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{16}{14})(p-\frac{9}{2})& =(\color{red}{x}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{2}x-\frac{8}{7}p+\frac{8}{7}.\frac{9}{2}& \text{Uitwerken } \\ & =px-\frac{9}{2}x-\frac{8}{7}p+\frac{72}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{9}{2}x-\frac{8}{7}p+\frac{36}{7} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-16}{5}-q)(\frac{4}{12}+b)& =(\color{red}{-q}+\color{orange}{\frac{-16}{5}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{3}q-\frac{16}{5}b-\frac{16}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =-bq-\frac{1}{3}q-\frac{16}{5}b-\frac{16}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{-10}{18})(20+x)& =(\color{red}{a}+\color{orange}{\frac{-5}{9}}).(\color{green}{x}+\color{blue}{20})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(20)} + \color{orange}{(\frac{-5}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = ax+20a-\frac{5}{9}x-\frac{5}{9}.20& \text{Uitwerken } \\ & =ax+20a-\frac{5}{9}x-\frac{100}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{15}{8}-p)(a+\frac{-8}{10})& =(\color{red}{-p}+\color{orange}{\frac{15}{8}}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{15}{8})} . \color{green}{(a)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{4}{5}p+\frac{15}{8}a-\frac{15}{8}.\frac{4}{5}& \text{Uitwerken } \\ & =-ap+\frac{4}{5}p+\frac{15}{8}a-\frac{60}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{4}{5}p+\frac{15}{8}a-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{11}{9}-x)(p-\frac{-15}{17})& =(\color{red}{-x}+\color{orange}{\frac{11}{9}}).(\color{green}{p}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{11}{9})} . \color{green}{(p)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{15}{17}x+\frac{11}{9}p+\frac{11}{9}.\frac{15}{17}& \text{Uitwerken } \\ & =-px-\frac{15}{17}x+\frac{11}{9}p+\frac{165}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{15}{17}x+\frac{11}{9}p+\frac{55}{51} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-20}{2}+x)(q+\frac{-1}{5})& =(\color{red}{x}+\color{orange}{(-10)}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(-10)} . \color{green}{(q)} + \color{orange}{(-10)} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{5}x-10q+10.\frac{1}{5}& \text{Uitwerken } \\ & =qx-\frac{1}{5}x-10q+\frac{10}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{5}x-10q+2 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(b+\frac{-14}{18})(a-\frac{13}{15})& =(\color{red}{b}+\color{orange}{\frac{-7}{9}}).(\color{green}{a}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{15}b-\frac{7}{9}a+\frac{7}{9}.\frac{13}{15}& \text{Uitwerken } \\ & =ab-\frac{13}{15}b-\frac{7}{9}a+\frac{91}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-6}{6}-p)(q+\frac{4}{10})& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{5}p-1q-1.\frac{2}{5}& \text{Uitwerken } \\ & =-pq-\frac{2}{5}p-1q-\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a+\frac{20}{6})(\frac{-4}{20}+x)& =(\color{red}{a}+\color{orange}{\frac{10}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{5}a+\frac{10}{3}x-\frac{10}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =ax-\frac{1}{5}a+\frac{10}{3}x-\frac{10}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{1}{5}a+\frac{10}{3}x-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)