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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{17}{9}-x)(p-\frac{12}{4})& =(\color{red}{-x}+\color{orange}{\frac{17}{9}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{17}{9})} . \color{green}{(p)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -px+3x+\frac{17}{9}p-\frac{17}{9}.3& \text{Uitwerken } \\ & =-px+3x+\frac{17}{9}p-\frac{51}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+3x+\frac{17}{9}p-\frac{17}{3} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(q-\frac{-4}{12})(p-\frac{10}{7})& =(\color{red}{q}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{7}q+\frac{1}{3}p-\frac{1}{3}.\frac{10}{7}& \text{Uitwerken } \\ & =pq-\frac{10}{7}q+\frac{1}{3}p-\frac{10}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{19}{7}+x)(\frac{9}{12}-q)& =(\color{red}{x}+\color{orange}{\frac{19}{7}}).(\color{green}{-q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{19}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{4}x-\frac{19}{7}q+\frac{19}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =-qx+\frac{3}{4}x-\frac{19}{7}q+\frac{57}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{1}{14}+p)(\frac{-12}{3}+q)& =(\color{red}{p}+\color{orange}{\frac{1}{14}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{1}{14})} . \color{green}{(q)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = pq-4p+\frac{1}{14}q-\frac{1}{14}.4& \text{Uitwerken } \\ & =pq-4p+\frac{1}{14}q-\frac{4}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-4p+\frac{1}{14}q-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-13}{12}+q)(x+\frac{-7}{12})& =(\color{red}{q}+\color{orange}{\frac{-13}{12}}).(\color{green}{x}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{12}q-\frac{13}{12}x+\frac{13}{12}.\frac{7}{12}& \text{Uitwerken } \\ & =qx-\frac{7}{12}q-\frac{13}{12}x+\frac{91}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x-\frac{-8}{18})(q+\frac{12}{19})& =(\color{red}{x}+\color{orange}{\frac{4}{9}}).(\color{green}{q}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{19}x+\frac{4}{9}q+\frac{4}{9}.\frac{12}{19}& \text{Uitwerken } \\ & =qx+\frac{12}{19}x+\frac{4}{9}q+\frac{48}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{19}x+\frac{4}{9}q+\frac{16}{57} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b+\frac{2}{18})(b+\frac{-17}{8})& =(\color{red}{b}+\color{orange}{\frac{1}{9}}).(\color{green}{b}+\color{blue}{\frac{-17}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{8})} + \color{orange}{(\frac{1}{9})} . \color{green}{(b)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-17}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{8}b+\frac{1}{9}b-\frac{1}{9}.\frac{17}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{8})+\frac{1}{9})b-(\frac{-17}{72}) & \text{Neem samen} \\ &=b^2-\frac{145}{72}b-(\frac{-17}{72}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(p+6)(\frac{10}{6}-q)& =(\color{red}{p}+\color{orange}{6}).(\color{green}{-q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(6)} . \color{green}{(-q)} + \color{orange}{(6)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{3}p-6q+6.\frac{5}{3}& \text{Uitwerken } \\ & =-pq+\frac{5}{3}p-6q+\frac{30}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{5}{3}p-6q+10 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q+\frac{3}{3})(q+\frac{19}{19})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qq+1q+1q+1.1& \text{Uitwerken } \\ & =q^2+(1+1)q+1 & \text{Neem samen} \\ &=q^2+2q+1 & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{17}{11}-p)(\frac{-20}{2}-p)& =(\color{red}{-p}+\color{orange}{\frac{17}{11}}).(\color{green}{-p}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(-10)} + \color{orange}{(\frac{17}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = pp+10p-\frac{17}{11}p-\frac{17}{11}.10& \text{Uitwerken } \\ & =p^2+(10+(\frac{-17}{11}))p-(\frac{-170}{11}) & \text{Neem samen} \\ &=p^2+\frac{93}{11}p-(\frac{-170}{11}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(x-\frac{-8}{20})(b+\frac{6}{6})& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x+\frac{2}{5}b+\frac{2}{5}.1& \text{Uitwerken } \\ & =bx+1x+\frac{2}{5}b+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-10}{10}-b)(p-\frac{19}{19})& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1b-1p+1.1& \text{Uitwerken } \\ & =-bp+1b-1p+1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)