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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{-3}{12})(q-\frac{19}{13})& =(\color{red}{x}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{13}x-\frac{1}{4}q+\frac{1}{4}.\frac{19}{13}& \text{Uitwerken } \\ & =qx-\frac{19}{13}x-\frac{1}{4}q+\frac{19}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-(-1))(\frac{-6}{10}+x)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{5}p+1x-1.\frac{3}{5}& \text{Uitwerken } \\ & =px-\frac{3}{5}p+1x-\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-16}{16}-b)(p-\frac{-3}{5})& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{5}b-1p-1.\frac{3}{5}& \text{Uitwerken } \\ & =-bp-\frac{3}{5}b-1p-\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a+\frac{-8}{12})(\frac{-16}{11}-b)& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{-b}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{16}{11}a+\frac{2}{3}b+\frac{2}{3}.\frac{16}{11}& \text{Uitwerken } \\ & =-ab-\frac{16}{11}a+\frac{2}{3}b+\frac{32}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{12}{8})(\frac{-13}{11}+a)& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{13}{11}a-\frac{3}{2}a+\frac{3}{2}.\frac{13}{11}& \text{Uitwerken } \\ & =a^2+((\frac{-13}{11})+(\frac{-3}{2}))a+\frac{39}{22} & \text{Neem samen} \\ &=a^2-\frac{59}{22}a+\frac{39}{22} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{15}{11}+q)(\frac{14}{9}+p)& =(\color{red}{q}+\color{orange}{\frac{15}{11}}).(\color{green}{p}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{15}{11})} . \color{green}{(p)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{14}{9}q+\frac{15}{11}p+\frac{15}{11}.\frac{14}{9}& \text{Uitwerken } \\ & =pq+\frac{14}{9}q+\frac{15}{11}p+\frac{210}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{14}{9}q+\frac{15}{11}p+\frac{70}{33} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-18}{6}+b)(p+\frac{-17}{15})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{17}{15}b-3p+3.\frac{17}{15}& \text{Uitwerken } \\ & =bp-\frac{17}{15}b-3p+\frac{51}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{17}{15}b-3p+\frac{17}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q+\frac{-8}{13})(b+\frac{-2}{4})& =(\color{red}{q}+\color{orange}{\frac{-8}{13}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-8}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{2}q-\frac{8}{13}b+\frac{8}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =bq-\frac{1}{2}q-\frac{8}{13}b+\frac{8}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{2}q-\frac{8}{13}b+\frac{4}{13} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a+\frac{-13}{16})(x+\frac{-16}{17})& =(\color{red}{a}+\color{orange}{\frac{-13}{16}}).(\color{green}{x}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{16}{17}a-\frac{13}{16}x+\frac{13}{16}.\frac{16}{17}& \text{Uitwerken } \\ & =ax-\frac{16}{17}a-\frac{13}{16}x+\frac{208}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{16}{17}a-\frac{13}{16}x+\frac{13}{17} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q-\frac{-8}{16})(\frac{14}{8}-b)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{-b}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{4}q-\frac{1}{2}b+\frac{1}{2}.\frac{7}{4}& \text{Uitwerken } \\ & =-bq+\frac{7}{4}q-\frac{1}{2}b+\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}((-5)+a)(\frac{9}{17}+x)& =(\color{red}{a}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{17}a-5x-5.\frac{9}{17}& \text{Uitwerken } \\ & =ax+\frac{9}{17}a-5x-\frac{45}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{-12}{4})(a-\frac{-20}{13})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{20}{13}b-3a-3.\frac{20}{13}& \text{Uitwerken } \\ & =ab+\frac{20}{13}b-3a-\frac{60}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)