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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{9}{6})(p+\frac{-5}{6})& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{6}a-\frac{3}{2}p+\frac{3}{2}.\frac{5}{6}& \text{Uitwerken } \\ & =ap-\frac{5}{6}a-\frac{3}{2}p+\frac{15}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{5}{6}a-\frac{3}{2}p+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x-\frac{5}{3})(p-\frac{-11}{10})& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{p}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{10}x-\frac{5}{3}p-\frac{5}{3}.\frac{11}{10}& \text{Uitwerken } \\ & =px+\frac{11}{10}x-\frac{5}{3}p-\frac{55}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{11}{10}x-\frac{5}{3}p-\frac{11}{6} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{12}{15}-x)(a+\frac{1}{12})& =(\color{red}{-x}+\color{orange}{\frac{4}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{12}x+\frac{4}{5}a+\frac{4}{5}.\frac{1}{12}& \text{Uitwerken } \\ & =-ax-\frac{1}{12}x+\frac{4}{5}a+\frac{4}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{1}{12}x+\frac{4}{5}a+\frac{1}{15} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-14}{19}-b)(a-(-4))& =(\color{red}{-b}+\color{orange}{\frac{-14}{19}}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(4)} + \color{orange}{(\frac{-14}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -ab-4b-\frac{14}{19}a-\frac{14}{19}.4& \text{Uitwerken } \\ & =-ab-4b-\frac{14}{19}a-\frac{56}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q+\frac{-4}{14})(q+\frac{10}{15})& =(\color{red}{q}+\color{orange}{\frac{-2}{7}}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{2}{3}q-\frac{2}{7}q-\frac{2}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =q^2+(\frac{2}{3}+(\frac{-2}{7}))q-(\frac{-4}{21}) & \text{Neem samen} \\ &=q^2+\frac{8}{21}q-(\frac{-4}{21}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(q+\frac{-18}{3})(b-\frac{13}{4})& =(\color{red}{q}+\color{orange}{(-6)}).(\color{green}{b}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(-6)} . \color{green}{(b)} + \color{orange}{(-6)} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{4}q-6b+6.\frac{13}{4}& \text{Uitwerken } \\ & =bq-\frac{13}{4}q-6b+\frac{78}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{13}{4}q-6b+\frac{39}{2} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-1}{8}+b)(\frac{5}{6}-p)& =(\color{red}{b}+\color{orange}{\frac{-1}{8}}).(\color{green}{-p}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{6}b+\frac{1}{8}p-\frac{1}{8}.\frac{5}{6}& \text{Uitwerken } \\ & =-bp+\frac{5}{6}b+\frac{1}{8}p-\frac{5}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{-18}{18})(\frac{-5}{3}+x)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{3}q+1x-1.\frac{5}{3}& \text{Uitwerken } \\ & =qx-\frac{5}{3}q+1x-\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{10}{3})((-3)-q)& =(\color{red}{x}+\color{orange}{\frac{-10}{3}}).(\color{green}{-q}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-10}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -qx-3x+\frac{10}{3}q+\frac{10}{3}.3& \text{Uitwerken } \\ & =-qx-3x+\frac{10}{3}q+\frac{30}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-3x+\frac{10}{3}q+10 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p-\frac{20}{8})(\frac{18}{16}-a)& =(\color{red}{p}+\color{orange}{\frac{-5}{2}}).(\color{green}{-a}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{8}p+\frac{5}{2}a-\frac{5}{2}.\frac{9}{8}& \text{Uitwerken } \\ & =-ap+\frac{9}{8}p+\frac{5}{2}a-\frac{45}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-5}{5}-b)(x-\frac{15}{13})& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{15}{13}b-1x+1.\frac{15}{13}& \text{Uitwerken } \\ & =-bx+\frac{15}{13}b-1x+\frac{15}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{-14}{19})(p+\frac{17}{10})& =(\color{red}{x}+\color{orange}{\frac{-14}{19}}).(\color{green}{p}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{10}x-\frac{14}{19}p-\frac{14}{19}.\frac{17}{10}& \text{Uitwerken } \\ & =px+\frac{17}{10}x-\frac{14}{19}p-\frac{238}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{17}{10}x-\frac{14}{19}p-\frac{119}{95} & \text{Vereenvoudig} \\\end{align}\)