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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{11}{19}-b)(p-\frac{-8}{6})& =(\color{red}{-b}+\color{orange}{\frac{11}{19}}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{11}{19})} . \color{green}{(p)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{3}b+\frac{11}{19}p+\frac{11}{19}.\frac{4}{3}& \text{Uitwerken } \\ & =-bp-\frac{4}{3}b+\frac{11}{19}p+\frac{44}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{4}{7})(\frac{-6}{2}+x)& =(\color{red}{p}+\color{orange}{\frac{-4}{7}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{-4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = px-3p-\frac{4}{7}x+\frac{4}{7}.3& \text{Uitwerken } \\ & =px-3p-\frac{4}{7}x+\frac{12}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{10}{5}-p)(q-\frac{-6}{3})& =(\color{red}{-p}+\color{orange}{2}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(2)} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -pq-2p+2q+2.2& \text{Uitwerken } \\ & =-pq-2p+2q+4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{-14}{8})(x+\frac{-18}{14})& =(\color{red}{p}+\color{orange}{\frac{-7}{4}}).(\color{green}{x}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{7}p-\frac{7}{4}x+\frac{7}{4}.\frac{9}{7}& \text{Uitwerken } \\ & =px-\frac{9}{7}p-\frac{7}{4}x+\frac{63}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{9}{7}p-\frac{7}{4}x+\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-6}{4}-q)(\frac{9}{12}-b)& =(\color{red}{-q}+\color{orange}{\frac{-3}{2}}).(\color{green}{-b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{4}q+\frac{3}{2}b-\frac{3}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =bq-\frac{3}{4}q+\frac{3}{2}b-\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x-\frac{8}{9})(\frac{-9}{15}-q)& =(\color{red}{x}+\color{orange}{\frac{-8}{9}}).(\color{green}{-q}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{5}x+\frac{8}{9}q+\frac{8}{9}.\frac{3}{5}& \text{Uitwerken } \\ & =-qx-\frac{3}{5}x+\frac{8}{9}q+\frac{24}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{3}{5}x+\frac{8}{9}q+\frac{8}{15} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{15}{3}+a)(a+(-9))& =(\color{red}{a}+\color{orange}{5}).(\color{green}{a}+\color{blue}{(-9)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-9)} + \color{orange}{(5)} . \color{green}{(a)} + \color{orange}{(5)} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = aa-9a+5a-5.9& \text{Uitwerken } \\ & =a^2+((-9)+5)a-(-45) & \text{Neem samen} \\ &=a^2-4a-(-45) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{-8}{8}-p)(\frac{-7}{14}+b)& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{2}p-1b+1.\frac{1}{2}& \text{Uitwerken } \\ & =-bp+\frac{1}{2}p-1b+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-19}{13}-x)(x-\frac{16}{3})& =(\color{red}{-x}+\color{orange}{\frac{-19}{13}}).(\color{green}{x}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{16}{3}x-\frac{19}{13}x+\frac{19}{13}.\frac{16}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{16}{3}+(\frac{-19}{13}))x+(\frac{-304}{39}) & \text{Neem samen} \\ &=-x^2+\frac{151}{39}x+(\frac{-304}{39}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(x+\frac{1}{3})(x+\frac{12}{10})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{6}{5}x+\frac{1}{3}x+\frac{1}{3}.\frac{6}{5}& \text{Uitwerken } \\ & =x^2+(\frac{6}{5}+\frac{1}{3})x+\frac{6}{15} & \text{Neem samen} \\ &=x^2+\frac{23}{15}x+\frac{6}{15} & \text{Maak de som} \\ &=x^2+\frac{23}{15}x+\frac{2}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(\frac{2}{20}+b)(x+\frac{-6}{12})& =(\color{red}{b}+\color{orange}{\frac{1}{10}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}b+\frac{1}{10}x-\frac{1}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}b+\frac{1}{10}x-\frac{1}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{9}{19})(\frac{-18}{8}+b)& =(\color{red}{b}+\color{orange}{\frac{9}{19}}).(\color{green}{b}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{9}{19})} . \color{green}{(b)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{9}{4}b+\frac{9}{19}b-\frac{9}{19}.\frac{9}{4}& \text{Uitwerken } \\ & =b^2+((\frac{-9}{4})+\frac{9}{19})b-(\frac{-81}{76}) & \text{Neem samen} \\ &=b^2-\frac{135}{76}b-(\frac{-81}{76}) & \text{Maak de som} \\\end{align}\)