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

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Werk uit en vereenvoudig

1. \((p+\frac{-10}{19})(x+\frac{-11}{5})\)
2. \((\frac{-11}{19}+a)(q+\frac{13}{15})\)
3. \((\frac{1}{3}+p)(x+\frac{-1}{6})\)
4. \((q-\frac{-1}{12})(\frac{1}{9}+q)\)
5. \((\frac{19}{3}+b)(b+\frac{-20}{16})\)
6. \((\frac{2}{17}-a)(x+\frac{12}{4})\)
7. \((q-\frac{-2}{6})(b-\frac{6}{14})\)
8. \((\frac{7}{8}-b)(b-\frac{17}{19})\)
9. \((b+\frac{-12}{3})(\frac{8}{12}+p)\)
10. \((\frac{-12}{2}+q)(x+\frac{18}{2})\)
11. \((\frac{-17}{14}-a)(b-\frac{-12}{19})\)
12. \((q+\frac{16}{19})(b+\frac{4}{11})\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-10}{19})(x+\frac{-11}{5})& =(\color{red}{p}+\color{orange}{\frac{-10}{19}}).(\color{green}{x}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{5}p-\frac{10}{19}x+\frac{10}{19}.\frac{11}{5}& \text{Uitwerken } \\ & =px-\frac{11}{5}p-\frac{10}{19}x+\frac{110}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{11}{5}p-\frac{10}{19}x+\frac{22}{19} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-11}{19}+a)(q+\frac{13}{15})& =(\color{red}{a}+\color{orange}{\frac{-11}{19}}).(\color{green}{q}+\color{blue}{\frac{13}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{15})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{13}{15})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{15}a-\frac{11}{19}q-\frac{11}{19}.\frac{13}{15}& \text{Uitwerken } \\ & =aq+\frac{13}{15}a-\frac{11}{19}q-\frac{143}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{1}{3}+p)(x+\frac{-1}{6})& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{6}p+\frac{1}{3}x-\frac{1}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =px-\frac{1}{6}p+\frac{1}{3}x-\frac{1}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{-1}{12})(\frac{1}{9}+q)& =(\color{red}{q}+\color{orange}{\frac{1}{12}}).(\color{green}{q}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{1}{12})} . \color{green}{(q)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{9}q+\frac{1}{12}q+\frac{1}{12}.\frac{1}{9}& \text{Uitwerken } \\ & =q^2+(\frac{1}{9}+\frac{1}{12})q+\frac{1}{108} & \text{Neem samen} \\ &=q^2+\frac{7}{36}q+\frac{1}{108} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(\frac{19}{3}+b)(b+\frac{-20}{16})& =(\color{red}{b}+\color{orange}{\frac{19}{3}}).(\color{green}{b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{19}{3})} . \color{green}{(b)} + \color{orange}{(\frac{19}{3})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{5}{4}b+\frac{19}{3}b-\frac{19}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =b^2+((\frac{-5}{4})+\frac{19}{3})b-(\frac{-95}{12}) & \text{Neem samen} \\ &=b^2+\frac{61}{12}b-(\frac{-95}{12}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{2}{17}-a)(x+\frac{12}{4})& =(\color{red}{-a}+\color{orange}{\frac{2}{17}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(3)} + \color{orange}{(\frac{2}{17})} . \color{green}{(x)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -ax-3a+\frac{2}{17}x+\frac{2}{17}.3& \text{Uitwerken } \\ & =-ax-3a+\frac{2}{17}x+\frac{6}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q-\frac{-2}{6})(b-\frac{6}{14})& =(\color{red}{q}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{7}q+\frac{1}{3}b-\frac{1}{3}.\frac{3}{7}& \text{Uitwerken } \\ & =bq-\frac{3}{7}q+\frac{1}{3}b-\frac{3}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{3}{7}q+\frac{1}{3}b-\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{7}{8}-b)(b-\frac{17}{19})& =(\color{red}{-b}+\color{orange}{\frac{7}{8}}).(\color{green}{b}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{7}{8})} . \color{green}{(b)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{17}{19}b+\frac{7}{8}b-\frac{7}{8}.\frac{17}{19}& \text{Uitwerken } \\ & =-b^2+(\frac{17}{19}+\frac{7}{8})b-\frac{119}{152} & \text{Neem samen} \\ &=-b^2+\frac{269}{152}b-\frac{119}{152} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(b+\frac{-12}{3})(\frac{8}{12}+p)& =(\color{red}{b}+\color{orange}{(-4)}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(-4)} . \color{green}{(p)} + \color{orange}{(-4)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{3}b-4p-4.\frac{2}{3}& \text{Uitwerken } \\ & =bp+\frac{2}{3}b-4p-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-12}{2}+q)(x+\frac{18}{2})& =(\color{red}{q}+\color{orange}{(-6)}).(\color{green}{x}+\color{blue}{9})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(9)} + \color{orange}{(-6)} . \color{green}{(x)} + \color{orange}{(-6)} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = qx+9q-6x-6.9& \text{Uitwerken } \\ & =qx+9q-6x-54 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-17}{14}-a)(b-\frac{-12}{19})& =(\color{red}{-a}+\color{orange}{\frac{-17}{14}}).(\color{green}{b}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{12}{19}a-\frac{17}{14}b-\frac{17}{14}.\frac{12}{19}& \text{Uitwerken } \\ & =-ab-\frac{12}{19}a-\frac{17}{14}b-\frac{204}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{12}{19}a-\frac{17}{14}b-\frac{102}{133} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q+\frac{16}{19})(b+\frac{4}{11})& =(\color{red}{q}+\color{orange}{\frac{16}{19}}).(\color{green}{b}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{16}{19})} . \color{green}{(b)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{11}q+\frac{16}{19}b+\frac{16}{19}.\frac{4}{11}& \text{Uitwerken } \\ & =bq+\frac{4}{11}q+\frac{16}{19}b+\frac{64}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)