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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{6}{12})(\frac{-15}{8}+a)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{8}q+\frac{1}{2}a-\frac{1}{2}.\frac{15}{8}& \text{Uitwerken } \\ & =aq-\frac{15}{8}q+\frac{1}{2}a-\frac{15}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{11}{18}+x)(\frac{4}{9}-a)& =(\color{red}{x}+\color{orange}{\frac{11}{18}}).(\color{green}{-a}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{11}{18})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{9}x-\frac{11}{18}a+\frac{11}{18}.\frac{4}{9}& \text{Uitwerken } \\ & =-ax+\frac{4}{9}x-\frac{11}{18}a+\frac{44}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{4}{9}x-\frac{11}{18}a+\frac{22}{81} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x-\frac{5}{4})(b+\frac{1}{2})& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}x-\frac{5}{4}b-\frac{5}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}x-\frac{5}{4}b-\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{-13}{18})(q-\frac{1}{14})& =(\color{red}{x}+\color{orange}{\frac{13}{18}}).(\color{green}{q}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{13}{18})} . \color{green}{(q)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{14}x+\frac{13}{18}q-\frac{13}{18}.\frac{1}{14}& \text{Uitwerken } \\ & =qx-\frac{1}{14}x+\frac{13}{18}q-\frac{13}{252} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{3}{3}-a)(b-\frac{4}{17})& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{4}{17}a+1b-1.\frac{4}{17}& \text{Uitwerken } \\ & =-ab+\frac{4}{17}a+1b-\frac{4}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{3}{19}+x)(\frac{17}{9}-b)& =(\color{red}{x}+\color{orange}{\frac{3}{19}}).(\color{green}{-b}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{3}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{19})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{17}{9}x-\frac{3}{19}b+\frac{3}{19}.\frac{17}{9}& \text{Uitwerken } \\ & =-bx+\frac{17}{9}x-\frac{3}{19}b+\frac{51}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{17}{9}x-\frac{3}{19}b+\frac{17}{57} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-17}{11}+p)(a+\frac{20}{17})& =(\color{red}{p}+\color{orange}{\frac{-17}{11}}).(\color{green}{a}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-17}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{20}{17}p-\frac{17}{11}a-\frac{17}{11}.\frac{20}{17}& \text{Uitwerken } \\ & =ap+\frac{20}{17}p-\frac{17}{11}a-\frac{340}{187} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{20}{17}p-\frac{17}{11}a-\frac{20}{11} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(a-\frac{-20}{18})(b+\frac{20}{13})& =(\color{red}{a}+\color{orange}{\frac{10}{9}}).(\color{green}{b}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{10}{9})} . \color{green}{(b)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{20}{13}a+\frac{10}{9}b+\frac{10}{9}.\frac{20}{13}& \text{Uitwerken } \\ & =ab+\frac{20}{13}a+\frac{10}{9}b+\frac{200}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{1}{12}+x)(14+b)& =(\color{red}{x}+\color{orange}{\frac{1}{12}}).(\color{green}{b}+\color{blue}{14})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(14)} + \color{orange}{(\frac{1}{12})} . \color{green}{(b)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = bx+14x+\frac{1}{12}b+\frac{1}{12}.14& \text{Uitwerken } \\ & =bx+14x+\frac{1}{12}b+\frac{14}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+14x+\frac{1}{12}b+\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a-\frac{-18}{7})(b-\frac{-1}{4})& =(\color{red}{a}+\color{orange}{\frac{18}{7}}).(\color{green}{b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{18}{7})} . \color{green}{(b)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{4}a+\frac{18}{7}b+\frac{18}{7}.\frac{1}{4}& \text{Uitwerken } \\ & =ab+\frac{1}{4}a+\frac{18}{7}b+\frac{18}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{4}a+\frac{18}{7}b+\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{4}{9}-b)(b-\frac{-20}{11})& =(\color{red}{-b}+\color{orange}{\frac{4}{9}}).(\color{green}{b}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{20}{11}b+\frac{4}{9}b+\frac{4}{9}.\frac{20}{11}& \text{Uitwerken } \\ & =-b^2+((\frac{-20}{11})+\frac{4}{9})b+(\frac{-80}{99}) & \text{Neem samen} \\ &=-b^2-\frac{136}{99}b+(\frac{-80}{99}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-15}{16}-q)(a+\frac{-6}{19})& =(\color{red}{-q}+\color{orange}{\frac{-15}{16}}).(\color{green}{a}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{6}{19}q-\frac{15}{16}a+\frac{15}{16}.\frac{6}{19}& \text{Uitwerken } \\ & =-aq+\frac{6}{19}q-\frac{15}{16}a+\frac{90}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{6}{19}q-\frac{15}{16}a+\frac{45}{152} & \text{Vereenvoudig} \\\end{align}\)