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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+(-10))(\frac{-3}{15}+q)& =(\color{red}{b}+\color{orange}{(-10)}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(-10)} . \color{green}{(q)} + \color{orange}{(-10)} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{5}b-10q+10.\frac{1}{5}& \text{Uitwerken } \\ & =bq-\frac{1}{5}b-10q+\frac{10}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{5}b-10q+2 & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-18}{19}+x)(\frac{7}{8}-q)& =(\color{red}{x}+\color{orange}{\frac{-18}{19}}).(\color{green}{-q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{7}{8}x+\frac{18}{19}q-\frac{18}{19}.\frac{7}{8}& \text{Uitwerken } \\ & =-qx+\frac{7}{8}x+\frac{18}{19}q-\frac{126}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{7}{8}x+\frac{18}{19}q-\frac{63}{76} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(6+x)(b-\frac{-18}{5})& =(\color{red}{x}+\color{orange}{6}).(\color{green}{b}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(6)} . \color{green}{(b)} + \color{orange}{(6)} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{18}{5}x+6b+6.\frac{18}{5}& \text{Uitwerken } \\ & =bx+\frac{18}{5}x+6b+\frac{108}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p-\frac{-7}{15})(\frac{-4}{3}+p)& =(\color{red}{p}+\color{orange}{\frac{7}{15}}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{7}{15})} . \color{green}{(p)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{3}p+\frac{7}{15}p-\frac{7}{15}.\frac{4}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{3})+\frac{7}{15})p-(\frac{-28}{45}) & \text{Neem samen} \\ &=p^2-\frac{13}{15}p-(\frac{-28}{45}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(a-\frac{-20}{12})(\frac{17}{3}+a)& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{17}{3}a+\frac{5}{3}a+\frac{5}{3}.\frac{17}{3}& \text{Uitwerken } \\ & =a^2+(\frac{17}{3}+\frac{5}{3})a+\frac{85}{9} & \text{Neem samen} \\ &=a^2+\frac{22}{3}a+\frac{85}{9} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(b-\frac{-8}{11})(p+\frac{10}{6})& =(\color{red}{b}+\color{orange}{\frac{8}{11}}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{8}{11})} . \color{green}{(p)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{3}b+\frac{8}{11}p+\frac{8}{11}.\frac{5}{3}& \text{Uitwerken } \\ & =bp+\frac{5}{3}b+\frac{8}{11}p+\frac{40}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-19}{20}-q)(\frac{11}{13}-b)& =(\color{red}{-q}+\color{orange}{\frac{-19}{20}}).(\color{green}{-b}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{13}q+\frac{19}{20}b-\frac{19}{20}.\frac{11}{13}& \text{Uitwerken } \\ & =bq-\frac{11}{13}q+\frac{19}{20}b-\frac{209}{260} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x-\frac{-12}{16})(b-\frac{-6}{16})& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{b}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{8}x+\frac{3}{4}b+\frac{3}{4}.\frac{3}{8}& \text{Uitwerken } \\ & =bx+\frac{3}{8}x+\frac{3}{4}b+\frac{9}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{6}{9}+q)(q+\frac{-12}{6})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qq-2q+\frac{2}{3}q-\frac{2}{3}.2& \text{Uitwerken } \\ & =q^2+((-2)+\frac{2}{3})q-(\frac{-4}{3}) & \text{Neem samen} \\ &=q^2-\frac{4}{3}q-(\frac{-4}{3}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{11}{18}+q)(b+\frac{-3}{2})& =(\color{red}{q}+\color{orange}{\frac{11}{18}}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{11}{18})} . \color{green}{(b)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{2}q+\frac{11}{18}b-\frac{11}{18}.\frac{3}{2}& \text{Uitwerken } \\ & =bq-\frac{3}{2}q+\frac{11}{18}b-\frac{33}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{3}{2}q+\frac{11}{18}b-\frac{11}{12} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{10}{9}-a)(\frac{-8}{5}-a)& =(\color{red}{-a}+\color{orange}{\frac{10}{9}}).(\color{green}{-a}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{10}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{8}{5}a-\frac{10}{9}a-\frac{10}{9}.\frac{8}{5}& \text{Uitwerken } \\ & =a^2+(\frac{8}{5}+(\frac{-10}{9}))a-(\frac{-80}{45}) & \text{Neem samen} \\ &=a^2+\frac{22}{45}a-(\frac{-80}{45}) & \text{Maak de som} \\ &=a^2+\frac{22}{45}a+\frac{16}{9} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
12. \(\begin{align}(\frac{-8}{13}+x)(a+\frac{7}{15})& =(\color{red}{x}+\color{orange}{\frac{-8}{13}}).(\color{green}{a}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-8}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{13})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{15}x-\frac{8}{13}a-\frac{8}{13}.\frac{7}{15}& \text{Uitwerken } \\ & =ax+\frac{7}{15}x-\frac{8}{13}a-\frac{56}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)