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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{5}{10}-a)(q+\frac{2}{20})& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{10}a+\frac{1}{2}q+\frac{1}{2}.\frac{1}{10}& \text{Uitwerken } \\ & =-aq-\frac{1}{10}a+\frac{1}{2}q+\frac{1}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a-\frac{14}{2})(x-\frac{-1}{19})& =(\color{red}{a}+\color{orange}{(-7)}).(\color{green}{x}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(-7)} . \color{green}{(x)} + \color{orange}{(-7)} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{19}a-7x-7.\frac{1}{19}& \text{Uitwerken } \\ & =ax+\frac{1}{19}a-7x-\frac{7}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-6}{14}+p)(p-2)& =(\color{red}{p}+\color{orange}{\frac{-3}{7}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pp-2p-\frac{3}{7}p+\frac{3}{7}.2& \text{Uitwerken } \\ & =p^2+((-2)+(\frac{-3}{7}))p+\frac{6}{7} & \text{Neem samen} \\ &=p^2-\frac{17}{7}p+\frac{6}{7} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{6}{8}-b)(\frac{14}{20}+x)& =(\color{red}{-b}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{7}{10}b+\frac{3}{4}x+\frac{3}{4}.\frac{7}{10}& \text{Uitwerken } \\ & =-bx-\frac{7}{10}b+\frac{3}{4}x+\frac{21}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-9}{12}-a)(\frac{3}{17}-x)& =(\color{red}{-a}+\color{orange}{\frac{-3}{4}}).(\color{green}{-x}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{17}a+\frac{3}{4}x-\frac{3}{4}.\frac{3}{17}& \text{Uitwerken } \\ & =ax-\frac{3}{17}a+\frac{3}{4}x-\frac{9}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{8}{8}-p)(b+\frac{1}{19})& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{19}p+1b+1.\frac{1}{19}& \text{Uitwerken } \\ & =-bp-\frac{1}{19}p+1b+\frac{1}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{7}{17}-x)(p+\frac{5}{20})& =(\color{red}{-x}+\color{orange}{\frac{7}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{7}{17})} . \color{green}{(p)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{4}x+\frac{7}{17}p+\frac{7}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =-px-\frac{1}{4}x+\frac{7}{17}p+\frac{7}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{14}{18})(x+\frac{12}{2})& =(\color{red}{b}+\color{orange}{\frac{-7}{9}}).(\color{green}{x}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(6)} + \color{orange}{(\frac{-7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bx+6b-\frac{7}{9}x-\frac{7}{9}.6& \text{Uitwerken } \\ & =bx+6b-\frac{7}{9}x-\frac{42}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+6b-\frac{7}{9}x-\frac{14}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q-\frac{-1}{18})(p+\frac{10}{19})& =(\color{red}{q}+\color{orange}{\frac{1}{18}}).(\color{green}{p}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{1}{18})} . \color{green}{(p)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{10}{19}q+\frac{1}{18}p+\frac{1}{18}.\frac{10}{19}& \text{Uitwerken } \\ & =pq+\frac{10}{19}q+\frac{1}{18}p+\frac{10}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{10}{19}q+\frac{1}{18}p+\frac{5}{171} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q-\frac{11}{19})(a-\frac{14}{7})& =(\color{red}{q}+\color{orange}{\frac{-11}{19}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aq-2q-\frac{11}{19}a+\frac{11}{19}.2& \text{Uitwerken } \\ & =aq-2q-\frac{11}{19}a+\frac{22}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-18}{3}+a)(\frac{2}{16}-a)& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{-a}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(-6)} . \color{green}{(-a)} + \color{orange}{(-6)} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{8}a+6a-6.\frac{1}{8}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{8}+6)a-\frac{6}{8} & \text{Neem samen} \\ &=-a^2+\frac{49}{8}a-\frac{6}{8} & \text{Maak de som} \\ &=-a^2+\frac{49}{8}a-\frac{3}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(\frac{4}{20}-p)(\frac{-6}{17}-b)& =(\color{red}{-p}+\color{orange}{\frac{1}{5}}).(\color{green}{-b}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{6}{17}p-\frac{1}{5}b-\frac{1}{5}.\frac{6}{17}& \text{Uitwerken } \\ & =bp+\frac{6}{17}p-\frac{1}{5}b-\frac{6}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)