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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-9}{13}-x)(\frac{-5}{16}+q)& =(\color{red}{-x}+\color{orange}{\frac{-9}{13}}).(\color{green}{q}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{16}x-\frac{9}{13}q+\frac{9}{13}.\frac{5}{16}& \text{Uitwerken } \\ & =-qx+\frac{5}{16}x-\frac{9}{13}q+\frac{45}{208} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{-10}{12})(\frac{15}{5}+b)& =(\color{red}{a}+\color{orange}{\frac{-5}{6}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{-5}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ab+3a-\frac{5}{6}b-\frac{5}{6}.3& \text{Uitwerken } \\ & =ab+3a-\frac{5}{6}b-\frac{15}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+3a-\frac{5}{6}b-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(p+\frac{-1}{6})(q+\frac{5}{8})& =(\color{red}{p}+\color{orange}{\frac{-1}{6}}).(\color{green}{q}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{8}p-\frac{1}{6}q-\frac{1}{6}.\frac{5}{8}& \text{Uitwerken } \\ & =pq+\frac{5}{8}p-\frac{1}{6}q-\frac{5}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{3}{4})(p-\frac{10}{15})& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{3}q-\frac{3}{4}p+\frac{3}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =pq-\frac{2}{3}q-\frac{3}{4}p+\frac{6}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{2}{3}q-\frac{3}{4}p+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-13}{17}+p)(p-\frac{-20}{9})& =(\color{red}{p}+\color{orange}{\frac{-13}{17}}).(\color{green}{p}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{20}{9}p-\frac{13}{17}p-\frac{13}{17}.\frac{20}{9}& \text{Uitwerken } \\ & =p^2+(\frac{20}{9}+(\frac{-13}{17}))p-(\frac{-260}{153}) & \text{Neem samen} \\ &=p^2+\frac{223}{153}p-(\frac{-260}{153}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-15}{13}+a)(\frac{-20}{18}-x)& =(\color{red}{a}+\color{orange}{\frac{-15}{13}}).(\color{green}{-x}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{10}{9}a+\frac{15}{13}x+\frac{15}{13}.\frac{10}{9}& \text{Uitwerken } \\ & =-ax-\frac{10}{9}a+\frac{15}{13}x+\frac{150}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{10}{9}a+\frac{15}{13}x+\frac{50}{39} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{5}{14}-x)(b+\frac{-12}{2})& =(\color{red}{-x}+\color{orange}{\frac{5}{14}}).(\color{green}{b}+\color{blue}{(-6)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(-6)} + \color{orange}{(\frac{5}{14})} . \color{green}{(b)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -bx+6x+\frac{5}{14}b-\frac{5}{14}.6& \text{Uitwerken } \\ & =-bx+6x+\frac{5}{14}b-\frac{30}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+6x+\frac{5}{14}b-\frac{15}{7} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(p-\frac{-8}{7})(\frac{-10}{2}+b)& =(\color{red}{p}+\color{orange}{\frac{8}{7}}).(\color{green}{b}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{8}{7})} . \color{green}{(b)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bp-5p+\frac{8}{7}b-\frac{8}{7}.5& \text{Uitwerken } \\ & =bp-5p+\frac{8}{7}b-\frac{40}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-8}{11}-a)(p+\frac{-4}{3})& =(\color{red}{-a}+\color{orange}{\frac{-8}{11}}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-8}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{4}{3}a-\frac{8}{11}p+\frac{8}{11}.\frac{4}{3}& \text{Uitwerken } \\ & =-ap+\frac{4}{3}a-\frac{8}{11}p+\frac{32}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-6}{16}+b)(\frac{-16}{6}+b)& =(\color{red}{b}+\color{orange}{\frac{-3}{8}}).(\color{green}{b}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{8}{3}b-\frac{3}{8}b+\frac{3}{8}.\frac{8}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-8}{3})+(\frac{-3}{8}))b+\frac{24}{24} & \text{Neem samen} \\ &=b^2-\frac{73}{24}b+\frac{24}{24} & \text{Maak de som} \\ &=b^2-\frac{73}{24}b+1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(\frac{-6}{7}+a)(q+\frac{20}{3})& =(\color{red}{a}+\color{orange}{\frac{-6}{7}}).(\color{green}{q}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{20}{3}a-\frac{6}{7}q-\frac{6}{7}.\frac{20}{3}& \text{Uitwerken } \\ & =aq+\frac{20}{3}a-\frac{6}{7}q-\frac{120}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{20}{3}a-\frac{6}{7}q-\frac{40}{7} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-5}{3}+q)(\frac{-20}{7}+a)& =(\color{red}{q}+\color{orange}{\frac{-5}{3}}).(\color{green}{a}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{20}{7}q-\frac{5}{3}a+\frac{5}{3}.\frac{20}{7}& \text{Uitwerken } \\ & =aq-\frac{20}{7}q-\frac{5}{3}a+\frac{100}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)