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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-6}{12})(\frac{-1}{8}-x)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{8}q-\frac{1}{2}x-\frac{1}{2}.\frac{1}{8}& \text{Uitwerken } \\ & =-qx-\frac{1}{8}q-\frac{1}{2}x-\frac{1}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{20}{11})(b-\frac{10}{20})& =(\color{red}{q}+\color{orange}{\frac{-20}{11}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{2}q-\frac{20}{11}b+\frac{20}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =bq-\frac{1}{2}q-\frac{20}{11}b+\frac{20}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{2}q-\frac{20}{11}b+\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q+\frac{-11}{5})(a-\frac{5}{2})& =(\color{red}{q}+\color{orange}{\frac{-11}{5}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{2}q-\frac{11}{5}a+\frac{11}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =aq-\frac{5}{2}q-\frac{11}{5}a+\frac{55}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{5}{2}q-\frac{11}{5}a+\frac{11}{2} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(x-\frac{-12}{2})(\frac{12}{2}+a)& =(\color{red}{x}+\color{orange}{6}).(\color{green}{a}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(6)} + \color{orange}{(6)} . \color{green}{(a)} + \color{orange}{(6)} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = ax+6x+6a+6.6& \text{Uitwerken } \\ & =ax+6x+6a+36 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{16}{20}-p)(b+\frac{11}{8})& =(\color{red}{-p}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{11}{8}p+\frac{4}{5}b+\frac{4}{5}.\frac{11}{8}& \text{Uitwerken } \\ & =-bp-\frac{11}{8}p+\frac{4}{5}b+\frac{44}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{11}{8}p+\frac{4}{5}b+\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-2}{13}+p)(\frac{-6}{14}+x)& =(\color{red}{p}+\color{orange}{\frac{-2}{13}}).(\color{green}{x}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{7}p-\frac{2}{13}x+\frac{2}{13}.\frac{3}{7}& \text{Uitwerken } \\ & =px-\frac{3}{7}p-\frac{2}{13}x+\frac{6}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b-\frac{-12}{16})(\frac{2}{7}-a)& =(\color{red}{b}+\color{orange}{\frac{3}{4}}).(\color{green}{-a}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{7}b-\frac{3}{4}a+\frac{3}{4}.\frac{2}{7}& \text{Uitwerken } \\ & =-ab+\frac{2}{7}b-\frac{3}{4}a+\frac{6}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{2}{7}b-\frac{3}{4}a+\frac{3}{14} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-6}{17}+p)(\frac{-6}{15}-x)& =(\color{red}{p}+\color{orange}{\frac{-6}{17}}).(\color{green}{-x}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{5}p+\frac{6}{17}x+\frac{6}{17}.\frac{2}{5}& \text{Uitwerken } \\ & =-px-\frac{2}{5}p+\frac{6}{17}x+\frac{12}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{10}{20})(\frac{8}{19}+p)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{8}{19}x+\frac{1}{2}p+\frac{1}{2}.\frac{8}{19}& \text{Uitwerken } \\ & =px+\frac{8}{19}x+\frac{1}{2}p+\frac{8}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{8}{19}x+\frac{1}{2}p+\frac{4}{19} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p+\frac{3}{13})(\frac{-12}{10}-a)& =(\color{red}{p}+\color{orange}{\frac{3}{13}}).(\color{green}{-a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{3}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{6}{5}p-\frac{3}{13}a-\frac{3}{13}.\frac{6}{5}& \text{Uitwerken } \\ & =-ap-\frac{6}{5}p-\frac{3}{13}a-\frac{18}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-11}{19}+a)(p+\frac{5}{8})& =(\color{red}{a}+\color{orange}{\frac{-11}{19}}).(\color{green}{p}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{8}a-\frac{11}{19}p-\frac{11}{19}.\frac{5}{8}& \text{Uitwerken } \\ & =ap+\frac{5}{8}a-\frac{11}{19}p-\frac{55}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{-18}{4})(b-\frac{-7}{13})& =(\color{red}{q}+\color{orange}{\frac{9}{2}}).(\color{green}{b}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{9}{2})} . \color{green}{(b)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{13}q+\frac{9}{2}b+\frac{9}{2}.\frac{7}{13}& \text{Uitwerken } \\ & =bq+\frac{7}{13}q+\frac{9}{2}b+\frac{63}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)