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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{1}{16})(\frac{-9}{14}-p)& =(\color{red}{b}+\color{orange}{\frac{-1}{16}}).(\color{green}{-p}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{9}{14}b+\frac{1}{16}p+\frac{1}{16}.\frac{9}{14}& \text{Uitwerken } \\ & =-bp-\frac{9}{14}b+\frac{1}{16}p+\frac{9}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{-9}{4})(b-\frac{-20}{20})& =(\color{red}{x}+\color{orange}{\frac{-9}{4}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-9}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x-\frac{9}{4}b-\frac{9}{4}.1& \text{Uitwerken } \\ & =bx+1x-\frac{9}{4}b-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}((-12)+p)(\frac{8}{20}+a)& =(\color{red}{p}+\color{orange}{(-12)}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(-12)} . \color{green}{(a)} + \color{orange}{(-12)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{5}p-12a-12.\frac{2}{5}& \text{Uitwerken } \\ & =ap+\frac{2}{5}p-12a-\frac{24}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-11}{14}-q)(p+\frac{-10}{16})& =(\color{red}{-q}+\color{orange}{\frac{-11}{14}}).(\color{green}{p}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{8}q-\frac{11}{14}p+\frac{11}{14}.\frac{5}{8}& \text{Uitwerken } \\ & =-pq+\frac{5}{8}q-\frac{11}{14}p+\frac{55}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q+\frac{18}{8})(\frac{18}{20}-a)& =(\color{red}{q}+\color{orange}{\frac{9}{4}}).(\color{green}{-a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{9}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{10}q-\frac{9}{4}a+\frac{9}{4}.\frac{9}{10}& \text{Uitwerken } \\ & =-aq+\frac{9}{10}q-\frac{9}{4}a+\frac{81}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q-\frac{5}{20})(x-\frac{4}{16})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{x}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{4}q-\frac{1}{4}x+\frac{1}{4}.\frac{1}{4}& \text{Uitwerken } \\ & =qx-\frac{1}{4}q-\frac{1}{4}x+\frac{1}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a+\frac{3}{5})(q-\frac{-13}{16})& =(\color{red}{a}+\color{orange}{\frac{3}{5}}).(\color{green}{q}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{16}a+\frac{3}{5}q+\frac{3}{5}.\frac{13}{16}& \text{Uitwerken } \\ & =aq+\frac{13}{16}a+\frac{3}{5}q+\frac{39}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{-19}{12})(\frac{13}{7}-x)& =(\color{red}{p}+\color{orange}{\frac{-19}{12}}).(\color{green}{-x}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{13}{7}p+\frac{19}{12}x-\frac{19}{12}.\frac{13}{7}& \text{Uitwerken } \\ & =-px+\frac{13}{7}p+\frac{19}{12}x-\frac{247}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{4}{13}-a)(\frac{-15}{8}+b)& =(\color{red}{-a}+\color{orange}{\frac{4}{13}}).(\color{green}{b}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{15}{8}a+\frac{4}{13}b-\frac{4}{13}.\frac{15}{8}& \text{Uitwerken } \\ & =-ab+\frac{15}{8}a+\frac{4}{13}b-\frac{60}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{15}{8}a+\frac{4}{13}b-\frac{15}{26} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(x+\frac{1}{11})(b-\frac{19}{7})& =(\color{red}{x}+\color{orange}{\frac{1}{11}}).(\color{green}{b}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{1}{11})} . \color{green}{(b)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{7}x+\frac{1}{11}b-\frac{1}{11}.\frac{19}{7}& \text{Uitwerken } \\ & =bx-\frac{19}{7}x+\frac{1}{11}b-\frac{19}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{-4}{9})(b+\frac{16}{19})& =(\color{red}{p}+\color{orange}{\frac{4}{9}}).(\color{green}{b}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{16}{19}p+\frac{4}{9}b+\frac{4}{9}.\frac{16}{19}& \text{Uitwerken } \\ & =bp+\frac{16}{19}p+\frac{4}{9}b+\frac{64}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{1}{16}+b)(x-\frac{-11}{3})& =(\color{red}{b}+\color{orange}{\frac{1}{16}}).(\color{green}{x}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{1}{16})} . \color{green}{(x)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{3}b+\frac{1}{16}x+\frac{1}{16}.\frac{11}{3}& \text{Uitwerken } \\ & =bx+\frac{11}{3}b+\frac{1}{16}x+\frac{11}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)