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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-13}{9})(\frac{-5}{8}-p)& =(\color{red}{b}+\color{orange}{\frac{-13}{9}}).(\color{green}{-p}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{5}{8}b+\frac{13}{9}p+\frac{13}{9}.\frac{5}{8}& \text{Uitwerken } \\ & =-bp-\frac{5}{8}b+\frac{13}{9}p+\frac{65}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-(-3))(\frac{-11}{13}-a)& =(\color{red}{x}+\color{orange}{3}).(\color{green}{-a}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(3)} . \color{green}{(-a)} + \color{orange}{(3)} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{13}x-3a-3.\frac{11}{13}& \text{Uitwerken } \\ & =-ax-\frac{11}{13}x-3a-\frac{33}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-10)(\frac{-15}{2}+q)& =(\color{red}{p}+\color{orange}{(-10)}).(\color{green}{q}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(-10)} . \color{green}{(q)} + \color{orange}{(-10)} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{15}{2}p-10q+10.\frac{15}{2}& \text{Uitwerken } \\ & =pq-\frac{15}{2}p-10q+\frac{150}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{15}{2}p-10q+75 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(x+\frac{15}{4})(\frac{-2}{3}+b)& =(\color{red}{x}+\color{orange}{\frac{15}{4}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{15}{4})} . \color{green}{(b)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{3}x+\frac{15}{4}b-\frac{15}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =bx-\frac{2}{3}x+\frac{15}{4}b-\frac{30}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{2}{3}x+\frac{15}{4}b-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(b-\frac{-2}{11})(a-\frac{-13}{6})& =(\color{red}{b}+\color{orange}{\frac{2}{11}}).(\color{green}{a}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{2}{11})} . \color{green}{(a)} + \color{orange}{(\frac{2}{11})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{6}b+\frac{2}{11}a+\frac{2}{11}.\frac{13}{6}& \text{Uitwerken } \\ & =ab+\frac{13}{6}b+\frac{2}{11}a+\frac{26}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{13}{6}b+\frac{2}{11}a+\frac{13}{33} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x-\frac{13}{19})((-4)-a)& =(\color{red}{x}+\color{orange}{\frac{-13}{19}}).(\color{green}{-a}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{-13}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ax-4x+\frac{13}{19}a+\frac{13}{19}.4& \text{Uitwerken } \\ & =-ax-4x+\frac{13}{19}a+\frac{52}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{16}{19})(x-\frac{-1}{13})& =(\color{red}{p}+\color{orange}{\frac{16}{19}}).(\color{green}{x}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{16}{19})} . \color{green}{(x)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{13}p+\frac{16}{19}x+\frac{16}{19}.\frac{1}{13}& \text{Uitwerken } \\ & =px+\frac{1}{13}p+\frac{16}{19}x+\frac{16}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-4}{8}+p)(b+6)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(6)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bp+6p-\frac{1}{2}b-\frac{1}{2}.6& \text{Uitwerken } \\ & =bp+6p-\frac{1}{2}b-\frac{6}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+6p-\frac{1}{2}b-3 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x+\frac{4}{5})(\frac{-12}{18}-p)& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{3}x-\frac{4}{5}p-\frac{4}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =-px-\frac{2}{3}x-\frac{4}{5}p-\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-15}{17}-p)(x-\frac{20}{7})& =(\color{red}{-p}+\color{orange}{\frac{-15}{17}}).(\color{green}{x}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{20}{7}p-\frac{15}{17}x+\frac{15}{17}.\frac{20}{7}& \text{Uitwerken } \\ & =-px+\frac{20}{7}p-\frac{15}{17}x+\frac{300}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{16}{14})(a-\frac{-3}{6})& =(\color{red}{x}+\color{orange}{\frac{8}{7}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{8}{7})} . \color{green}{(a)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}x+\frac{8}{7}a+\frac{8}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}x+\frac{8}{7}a+\frac{8}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{2}x+\frac{8}{7}a+\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{4}{7}+x)(q-\frac{-7}{13})& =(\color{red}{x}+\color{orange}{\frac{4}{7}}).(\color{green}{q}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{13}x+\frac{4}{7}q+\frac{4}{7}.\frac{7}{13}& \text{Uitwerken } \\ & =qx+\frac{7}{13}x+\frac{4}{7}q+\frac{28}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{7}{13}x+\frac{4}{7}q+\frac{4}{13} & \text{Vereenvoudig} \\\end{align}\)