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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{16}{6}-a)((-10)+x)& =(\color{red}{-a}+\color{orange}{\frac{8}{3}}).(\color{green}{x}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(-10)} + \color{orange}{(\frac{8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -ax+10a+\frac{8}{3}x-\frac{8}{3}.10& \text{Uitwerken } \\ & =-ax+10a+\frac{8}{3}x-\frac{80}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-4}{17}+b)(\frac{-10}{3}-a)& =(\color{red}{b}+\color{orange}{\frac{-4}{17}}).(\color{green}{-a}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{-4}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{10}{3}b+\frac{4}{17}a+\frac{4}{17}.\frac{10}{3}& \text{Uitwerken } \\ & =-ab-\frac{10}{3}b+\frac{4}{17}a+\frac{40}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{16}{11}+p)(\frac{16}{17}+q)& =(\color{red}{p}+\color{orange}{\frac{16}{11}}).(\color{green}{q}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{16}{11})} . \color{green}{(q)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{16}{17}p+\frac{16}{11}q+\frac{16}{11}.\frac{16}{17}& \text{Uitwerken } \\ & =pq+\frac{16}{17}p+\frac{16}{11}q+\frac{256}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p-\frac{1}{18})(p-(-3))& =(\color{red}{p}+\color{orange}{\frac{-1}{18}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{-1}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = pp+3p-\frac{1}{18}p-\frac{1}{18}.3& \text{Uitwerken } \\ & =p^2+(3+(\frac{-1}{18}))p-(\frac{-3}{18}) & \text{Neem samen} \\ &=p^2+\frac{53}{18}p-(\frac{-3}{18}) & \text{Maak de som} \\ &=p^2+\frac{53}{18}p+\frac{1}{6} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
5. \(\begin{align}(p-\frac{9}{17})(\frac{15}{7}-b)& =(\color{red}{p}+\color{orange}{\frac{-9}{17}}).(\color{green}{-b}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{15}{7}p+\frac{9}{17}b-\frac{9}{17}.\frac{15}{7}& \text{Uitwerken } \\ & =-bp+\frac{15}{7}p+\frac{9}{17}b-\frac{135}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-2}{9}-x)(\frac{5}{14}-q)& =(\color{red}{-x}+\color{orange}{\frac{-2}{9}}).(\color{green}{-q}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{14}x+\frac{2}{9}q-\frac{2}{9}.\frac{5}{14}& \text{Uitwerken } \\ & =qx-\frac{5}{14}x+\frac{2}{9}q-\frac{10}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{14}x+\frac{2}{9}q-\frac{5}{63} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b-\frac{-1}{11})(\frac{-17}{17}+x)& =(\color{red}{b}+\color{orange}{\frac{1}{11}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{11})} . \color{green}{(x)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx-1b+\frac{1}{11}x-\frac{1}{11}.1& \text{Uitwerken } \\ & =bx-1b+\frac{1}{11}x-\frac{1}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{19}{12})(\frac{15}{2}-q)& =(\color{red}{b}+\color{orange}{\frac{-19}{12}}).(\color{green}{-q}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{15}{2}b+\frac{19}{12}q-\frac{19}{12}.\frac{15}{2}& \text{Uitwerken } \\ & =-bq+\frac{15}{2}b+\frac{19}{12}q-\frac{285}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{15}{2}b+\frac{19}{12}q-\frac{95}{8} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x-\frac{19}{14})(\frac{-19}{11}-b)& =(\color{red}{x}+\color{orange}{\frac{-19}{14}}).(\color{green}{-b}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{19}{11}x+\frac{19}{14}b+\frac{19}{14}.\frac{19}{11}& \text{Uitwerken } \\ & =-bx-\frac{19}{11}x+\frac{19}{14}b+\frac{361}{154} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{10}{17}+a)(\frac{-8}{19}+q)& =(\color{red}{a}+\color{orange}{\frac{10}{17}}).(\color{green}{q}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{10}{17})} . \color{green}{(q)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{8}{19}a+\frac{10}{17}q-\frac{10}{17}.\frac{8}{19}& \text{Uitwerken } \\ & =aq-\frac{8}{19}a+\frac{10}{17}q-\frac{80}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{1}{11}+a)(b-\frac{-6}{13})& =(\color{red}{a}+\color{orange}{\frac{1}{11}}).(\color{green}{b}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{1}{11})} . \color{green}{(b)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{6}{13}a+\frac{1}{11}b+\frac{1}{11}.\frac{6}{13}& \text{Uitwerken } \\ & =ab+\frac{6}{13}a+\frac{1}{11}b+\frac{6}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{20}{20}+q)(a-\frac{-6}{11})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{11}q+1a+1.\frac{6}{11}& \text{Uitwerken } \\ & =aq+\frac{6}{11}q+1a+\frac{6}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)