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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-20}{5}-x)(q+\frac{11}{13})& =(\color{red}{-x}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{11}{13}x-4q-4.\frac{11}{13}& \text{Uitwerken } \\ & =-qx-\frac{11}{13}x-4q-\frac{44}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-8}{7}+q)(\frac{15}{4}+q)& =(\color{red}{q}+\color{orange}{\frac{-8}{7}}).(\color{green}{q}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{15}{4}q-\frac{8}{7}q-\frac{8}{7}.\frac{15}{4}& \text{Uitwerken } \\ & =q^2+(\frac{15}{4}+(\frac{-8}{7}))q-(\frac{-120}{28}) & \text{Neem samen} \\ &=q^2+\frac{73}{28}q-(\frac{-120}{28}) & \text{Maak de som} \\ &=q^2+\frac{73}{28}q+\frac{30}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
3. \(\begin{align}(\frac{6}{10}+p)((-14)-x)& =(\color{red}{p}+\color{orange}{\frac{3}{5}}).(\color{green}{-x}+\color{blue}{(-14)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(-14)} + \color{orange}{(\frac{3}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = -px-14p-\frac{3}{5}x-\frac{3}{5}.14& \text{Uitwerken } \\ & =-px-14p-\frac{3}{5}x-\frac{42}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{-5}{11})(\frac{-10}{3}+b)& =(\color{red}{x}+\color{orange}{\frac{-5}{11}}).(\color{green}{b}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{10}{3}x-\frac{5}{11}b+\frac{5}{11}.\frac{10}{3}& \text{Uitwerken } \\ & =bx-\frac{10}{3}x-\frac{5}{11}b+\frac{50}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-13}{20}+a)(b+\frac{-7}{3})& =(\color{red}{a}+\color{orange}{\frac{-13}{20}}).(\color{green}{b}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{3}a-\frac{13}{20}b+\frac{13}{20}.\frac{7}{3}& \text{Uitwerken } \\ & =ab-\frac{7}{3}a-\frac{13}{20}b+\frac{91}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{13}{9}+a)(\frac{13}{10}+q)& =(\color{red}{a}+\color{orange}{\frac{13}{9}}).(\color{green}{q}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{13}{9})} . \color{green}{(q)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{10}a+\frac{13}{9}q+\frac{13}{9}.\frac{13}{10}& \text{Uitwerken } \\ & =aq+\frac{13}{10}a+\frac{13}{9}q+\frac{169}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(13-b)(\frac{-3}{6}-x)& =(\color{red}{-b}+\color{orange}{13}).(\color{green}{-x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(13)} . \color{green}{(-x)} + \color{orange}{(13)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}b-13x-13.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}b-13x-\frac{13}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x-\frac{-2}{3})(b-\frac{-15}{7})& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{7}x+\frac{2}{3}b+\frac{2}{3}.\frac{15}{7}& \text{Uitwerken } \\ & =bx+\frac{15}{7}x+\frac{2}{3}b+\frac{30}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{7}x+\frac{2}{3}b+\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{5}{20}+q)(p+\frac{-14}{10})& =(\color{red}{q}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{5}q+\frac{1}{4}p-\frac{1}{4}.\frac{7}{5}& \text{Uitwerken } \\ & =pq-\frac{7}{5}q+\frac{1}{4}p-\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-2}{17}+q)((-11)-b)& =(\color{red}{q}+\color{orange}{\frac{-2}{17}}).(\color{green}{-b}+\color{blue}{(-11)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(-11)} + \color{orange}{(\frac{-2}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = -bq-11q+\frac{2}{17}b+\frac{2}{17}.11& \text{Uitwerken } \\ & =-bq-11q+\frac{2}{17}b+\frac{22}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-8}{4}+x)(\frac{-10}{9}-q)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{10}{9}x+2q+2.\frac{10}{9}& \text{Uitwerken } \\ & =-qx-\frac{10}{9}x+2q+\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{1}{6}+p)(q+11)& =(\color{red}{p}+\color{orange}{\frac{1}{6}}).(\color{green}{q}+\color{blue}{11})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(11)} + \color{orange}{(\frac{1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = pq+11p+\frac{1}{6}q+\frac{1}{6}.11& \text{Uitwerken } \\ & =pq+11p+\frac{1}{6}q+\frac{11}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)