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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{6}{5}-a)(\frac{11}{11}-q)& =(\color{red}{-a}+\color{orange}{\frac{6}{5}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(1)} + \color{orange}{(\frac{6}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a-\frac{6}{5}q+\frac{6}{5}.1& \text{Uitwerken } \\ & =aq-1a-\frac{6}{5}q+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{19}{19}+q)(a+\frac{10}{2})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = aq+5q+1a+1.5& \text{Uitwerken } \\ & =aq+5q+1a+5 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a+\frac{-12}{10})(\frac{-7}{13}+x)& =(\color{red}{a}+\color{orange}{\frac{-6}{5}}).(\color{green}{x}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{13}a-\frac{6}{5}x+\frac{6}{5}.\frac{7}{13}& \text{Uitwerken } \\ & =ax-\frac{7}{13}a-\frac{6}{5}x+\frac{42}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{-7}{8})(p-\frac{-2}{17})& =(\color{red}{x}+\color{orange}{\frac{7}{8}}).(\color{green}{p}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{2}{17}x+\frac{7}{8}p+\frac{7}{8}.\frac{2}{17}& \text{Uitwerken } \\ & =px+\frac{2}{17}x+\frac{7}{8}p+\frac{14}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{2}{17}x+\frac{7}{8}p+\frac{7}{68} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p-\frac{10}{8})(\frac{-1}{11}+b)& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{11}p-\frac{5}{4}b+\frac{5}{4}.\frac{1}{11}& \text{Uitwerken } \\ & =bp-\frac{1}{11}p-\frac{5}{4}b+\frac{5}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{2}{13}-b)(\frac{-3}{2}+x)& =(\color{red}{-b}+\color{orange}{\frac{2}{13}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{2}b+\frac{2}{13}x-\frac{2}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =-bx+\frac{3}{2}b+\frac{2}{13}x-\frac{6}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{3}{2}b+\frac{2}{13}x-\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(x+\frac{5}{6})(\frac{-3}{4}+q)& =(\color{red}{x}+\color{orange}{\frac{5}{6}}).(\color{green}{q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{4}x+\frac{5}{6}q-\frac{5}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =qx-\frac{3}{4}x+\frac{5}{6}q-\frac{15}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{3}{4}x+\frac{5}{6}q-\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{6}{17}+x)(b-(-12))& =(\color{red}{x}+\color{orange}{\frac{6}{17}}).(\color{green}{b}+\color{blue}{12})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(12)} + \color{orange}{(\frac{6}{17})} . \color{green}{(b)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = bx+12x+\frac{6}{17}b+\frac{6}{17}.12& \text{Uitwerken } \\ & =bx+12x+\frac{6}{17}b+\frac{72}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q-\frac{-2}{13})(\frac{-1}{2}-p)& =(\color{red}{q}+\color{orange}{\frac{2}{13}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{2}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{2}q-\frac{2}{13}p-\frac{2}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =-pq-\frac{1}{2}q-\frac{2}{13}p-\frac{2}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{1}{2}q-\frac{2}{13}p-\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(1-q)(\frac{11}{13}+p)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{11}{13}q+1p+1.\frac{11}{13}& \text{Uitwerken } \\ & =-pq-\frac{11}{13}q+1p+\frac{11}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{-15}{3})(\frac{-14}{11}+b)& =(\color{red}{p}+\color{orange}{5}).(\color{green}{b}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(5)} . \color{green}{(b)} + \color{orange}{(5)} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{14}{11}p+5b-5.\frac{14}{11}& \text{Uitwerken } \\ & =bp-\frac{14}{11}p+5b-\frac{70}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{10}{10}-b)(p+\frac{-10}{19})& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{10}{19}b+1p-1.\frac{10}{19}& \text{Uitwerken } \\ & =-bp+\frac{10}{19}b+1p-\frac{10}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)