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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{15}{10}+a)(\frac{10}{17}+a)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{10}{17}a+\frac{3}{2}a+\frac{3}{2}.\frac{10}{17}& \text{Uitwerken } \\ & =a^2+(\frac{10}{17}+\frac{3}{2})a+\frac{30}{34} & \text{Neem samen} \\ &=a^2+\frac{71}{34}a+\frac{30}{34} & \text{Maak de som} \\ &=a^2+\frac{71}{34}a+\frac{15}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(p-\frac{-6}{11})(\frac{-9}{15}+a)& =(\color{red}{p}+\color{orange}{\frac{6}{11}}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{6}{11})} . \color{green}{(a)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{5}p+\frac{6}{11}a-\frac{6}{11}.\frac{3}{5}& \text{Uitwerken } \\ & =ap-\frac{3}{5}p+\frac{6}{11}a-\frac{18}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{20}{10}-q)(13+b)& =(\color{red}{-q}+\color{orange}{2}).(\color{green}{b}+\color{blue}{13})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(13)} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = -bq-13q+2b+2.13& \text{Uitwerken } \\ & =-bq-13q+2b+26 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-16}{7}+p)(\frac{-3}{6}-p)& =(\color{red}{p}+\color{orange}{\frac{-16}{7}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{2}p+\frac{16}{7}p+\frac{16}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{2})+\frac{16}{7})p+(\frac{-16}{14}) & \text{Neem samen} \\ &=-p^2+\frac{25}{14}p+(\frac{-16}{14}) & \text{Maak de som} \\ &=-p^2+\frac{25}{14}p+(\frac{-8}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(\frac{11}{5}+x)(\frac{-6}{4}+b)& =(\color{red}{x}+\color{orange}{\frac{11}{5}}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{11}{5})} . \color{green}{(b)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{2}x+\frac{11}{5}b-\frac{11}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =bx-\frac{3}{2}x+\frac{11}{5}b-\frac{33}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{15}{3}-b)(x-\frac{16}{5})& =(\color{red}{-b}+\color{orange}{5}).(\color{green}{x}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{16}{5}b+5x-5.\frac{16}{5}& \text{Uitwerken } \\ & =-bx+\frac{16}{5}b+5x-\frac{80}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{16}{5}b+5x-16 & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-17}{3}+b)(q-\frac{13}{20})& =(\color{red}{b}+\color{orange}{\frac{-17}{3}}).(\color{green}{q}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{20}b-\frac{17}{3}q+\frac{17}{3}.\frac{13}{20}& \text{Uitwerken } \\ & =bq-\frac{13}{20}b-\frac{17}{3}q+\frac{221}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-1}{7}+x)(a-\frac{-11}{2})& =(\color{red}{x}+\color{orange}{\frac{-1}{7}}).(\color{green}{a}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{2}x-\frac{1}{7}a-\frac{1}{7}.\frac{11}{2}& \text{Uitwerken } \\ & =ax+\frac{11}{2}x-\frac{1}{7}a-\frac{11}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q-\frac{-18}{16})(q-16)& =(\color{red}{q}+\color{orange}{\frac{9}{8}}).(\color{green}{q}+\color{blue}{(-16)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-16)} + \color{orange}{(\frac{9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = qq-16q+\frac{9}{8}q-\frac{9}{8}.16& \text{Uitwerken } \\ & =q^2+((-16)+\frac{9}{8})q-(\frac{-144}{8}) & \text{Neem samen} \\ &=q^2-\frac{119}{8}q-(\frac{-144}{8}) & \text{Maak de som} \\ &=q^2-\frac{119}{8}q+18 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
10. \(\begin{align}(b+\frac{-20}{13})(x-\frac{-17}{17})& =(\color{red}{b}+\color{orange}{\frac{-20}{13}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-20}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1b-\frac{20}{13}x-\frac{20}{13}.1& \text{Uitwerken } \\ & =bx+1b-\frac{20}{13}x-\frac{20}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{-11}{12})(x-\frac{-10}{6})& =(\color{red}{x}+\color{orange}{\frac{-11}{12}}).(\color{green}{x}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{5}{3}x-\frac{11}{12}x-\frac{11}{12}.\frac{5}{3}& \text{Uitwerken } \\ & =x^2+(\frac{5}{3}+(\frac{-11}{12}))x-(\frac{-55}{36}) & \text{Neem samen} \\ &=x^2+\frac{9}{12}x-(\frac{-55}{36}) & \text{Maak de som} \\ &=x^2+\frac{3}{4}x+\frac{55}{36} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
12. \(\begin{align}(\frac{10}{11}+x)(a-\frac{7}{7})& =(\color{red}{x}+\color{orange}{\frac{10}{11}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{10}{11})} . \color{green}{(a)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x+\frac{10}{11}a-\frac{10}{11}.1& \text{Uitwerken } \\ & =ax-1x+\frac{10}{11}a-\frac{10}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)