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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-12}{3}+q)(\frac{12}{4}+a)& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = aq+3q-4a-4.3& \text{Uitwerken } \\ & =aq+3q-4a-12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{6}{4})(x+\frac{-8}{6})& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{3}b+\frac{3}{2}x-\frac{3}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =bx-\frac{4}{3}b+\frac{3}{2}x-\frac{12}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{4}{3}b+\frac{3}{2}x-2 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(15+x)(a-\frac{-10}{15})& =(\color{red}{x}+\color{orange}{15}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(15)} . \color{green}{(a)} + \color{orange}{(15)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}x+15a+15.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}x+15a+\frac{30}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{3}x+15a+10 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(x+\frac{17}{2})(11-a)& =(\color{red}{x}+\color{orange}{\frac{17}{2}}).(\color{green}{-a}+\color{blue}{11})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(11)} + \color{orange}{(\frac{17}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = -ax+11x-\frac{17}{2}a+\frac{17}{2}.11& \text{Uitwerken } \\ & =-ax+11x-\frac{17}{2}a+\frac{187}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{13}{11}+q)(b+(-5))& =(\color{red}{q}+\color{orange}{\frac{13}{11}}).(\color{green}{b}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-5)} + \color{orange}{(\frac{13}{11})} . \color{green}{(b)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bq-5q+\frac{13}{11}b-\frac{13}{11}.5& \text{Uitwerken } \\ & =bq-5q+\frac{13}{11}b-\frac{65}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{20}{20}-x)(x-\frac{10}{13})& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{10}{13}x+1x-1.\frac{10}{13}& \text{Uitwerken } \\ & =-x^2+(\frac{10}{13}+1)x-\frac{10}{13} & \text{Neem samen} \\ &=-x^2+\frac{23}{13}x-\frac{10}{13} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(p-\frac{17}{18})(a+\frac{13}{12})& =(\color{red}{p}+\color{orange}{\frac{-17}{18}}).(\color{green}{a}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{12}p-\frac{17}{18}a-\frac{17}{18}.\frac{13}{12}& \text{Uitwerken } \\ & =ap+\frac{13}{12}p-\frac{17}{18}a-\frac{221}{216} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{13}{15}+q)(\frac{-5}{12}+a)& =(\color{red}{q}+\color{orange}{\frac{13}{15}}).(\color{green}{a}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{13}{15})} . \color{green}{(a)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{12}q+\frac{13}{15}a-\frac{13}{15}.\frac{5}{12}& \text{Uitwerken } \\ & =aq-\frac{5}{12}q+\frac{13}{15}a-\frac{65}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{5}{12}q+\frac{13}{15}a-\frac{13}{36} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-17}{5}-x)(b+\frac{-8}{20})& =(\color{red}{-x}+\color{orange}{\frac{-17}{5}}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{2}{5}x-\frac{17}{5}b+\frac{17}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =-bx+\frac{2}{5}x-\frac{17}{5}b+\frac{34}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-14}{12})(a+\frac{-20}{19})& =(\color{red}{x}+\color{orange}{\frac{7}{6}}).(\color{green}{a}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{7}{6})} . \color{green}{(a)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{20}{19}x+\frac{7}{6}a-\frac{7}{6}.\frac{20}{19}& \text{Uitwerken } \\ & =ax-\frac{20}{19}x+\frac{7}{6}a-\frac{140}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{20}{19}x+\frac{7}{6}a-\frac{70}{57} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q+\frac{14}{9})(p-\frac{-15}{9})& =(\color{red}{q}+\color{orange}{\frac{14}{9}}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{14}{9})} . \color{green}{(p)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{3}q+\frac{14}{9}p+\frac{14}{9}.\frac{5}{3}& \text{Uitwerken } \\ & =pq+\frac{5}{3}q+\frac{14}{9}p+\frac{70}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{9}{16}-x)(a-\frac{-6}{8})& =(\color{red}{-x}+\color{orange}{\frac{9}{16}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{9}{16})} . \color{green}{(a)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{4}x+\frac{9}{16}a+\frac{9}{16}.\frac{3}{4}& \text{Uitwerken } \\ & =-ax-\frac{3}{4}x+\frac{9}{16}a+\frac{27}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)