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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{16}{13}-b)(\frac{-16}{18}+a)& =(\color{red}{-b}+\color{orange}{\frac{16}{13}}).(\color{green}{a}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{16}{13})} . \color{green}{(a)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{8}{9}b+\frac{16}{13}a-\frac{16}{13}.\frac{8}{9}& \text{Uitwerken } \\ & =-ab+\frac{8}{9}b+\frac{16}{13}a-\frac{128}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{13}{19}-x)(q-\frac{-10}{13})& =(\color{red}{-x}+\color{orange}{\frac{13}{19}}).(\color{green}{q}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(\frac{13}{19})} . \color{green}{(q)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{10}{13}x+\frac{13}{19}q+\frac{13}{19}.\frac{10}{13}& \text{Uitwerken } \\ & =-qx-\frac{10}{13}x+\frac{13}{19}q+\frac{130}{247} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{10}{13}x+\frac{13}{19}q+\frac{10}{19} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x-\frac{-18}{11})(\frac{12}{9}+x)& =(\color{red}{x}+\color{orange}{\frac{18}{11}}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{18}{11})} . \color{green}{(x)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{4}{3}x+\frac{18}{11}x+\frac{18}{11}.\frac{4}{3}& \text{Uitwerken } \\ & =x^2+(\frac{4}{3}+\frac{18}{11})x+\frac{72}{33} & \text{Neem samen} \\ &=x^2+\frac{98}{33}x+\frac{72}{33} & \text{Maak de som} \\ &=x^2+\frac{98}{33}x+\frac{24}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(a-\frac{-3}{4})(p-\frac{-18}{17})& =(\color{red}{a}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{18}{17}a+\frac{3}{4}p+\frac{3}{4}.\frac{18}{17}& \text{Uitwerken } \\ & =ap+\frac{18}{17}a+\frac{3}{4}p+\frac{54}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{18}{17}a+\frac{3}{4}p+\frac{27}{34} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(a-\frac{-1}{3})(b-\frac{5}{20})& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{4}a+\frac{1}{3}b-\frac{1}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =ab-\frac{1}{4}a+\frac{1}{3}b-\frac{1}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-4}{7}+p)(a+\frac{-16}{9})& =(\color{red}{p}+\color{orange}{\frac{-4}{7}}).(\color{green}{a}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{16}{9}p-\frac{4}{7}a+\frac{4}{7}.\frac{16}{9}& \text{Uitwerken } \\ & =ap-\frac{16}{9}p-\frac{4}{7}a+\frac{64}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{-14}{19})(b+\frac{3}{13})& =(\color{red}{q}+\color{orange}{\frac{-14}{19}}).(\color{green}{b}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{13}q-\frac{14}{19}b-\frac{14}{19}.\frac{3}{13}& \text{Uitwerken } \\ & =bq+\frac{3}{13}q-\frac{14}{19}b-\frac{42}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-8}{11}+x)(\frac{-1}{12}-a)& =(\color{red}{x}+\color{orange}{\frac{-8}{11}}).(\color{green}{-a}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{-8}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{12}x+\frac{8}{11}a+\frac{8}{11}.\frac{1}{12}& \text{Uitwerken } \\ & =-ax-\frac{1}{12}x+\frac{8}{11}a+\frac{8}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{1}{12}x+\frac{8}{11}a+\frac{2}{33} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q+\frac{12}{5})(\frac{15}{4}+b)& =(\color{red}{q}+\color{orange}{\frac{12}{5}}).(\color{green}{b}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{12}{5})} . \color{green}{(b)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{4}q+\frac{12}{5}b+\frac{12}{5}.\frac{15}{4}& \text{Uitwerken } \\ & =bq+\frac{15}{4}q+\frac{12}{5}b+\frac{180}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{15}{4}q+\frac{12}{5}b+9 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-7}{20}+q)((-15)+a)& =(\color{red}{q}+\color{orange}{\frac{-7}{20}}).(\color{green}{a}+\color{blue}{(-15)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-15)} + \color{orange}{(\frac{-7}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = aq-15q-\frac{7}{20}a+\frac{7}{20}.15& \text{Uitwerken } \\ & =aq-15q-\frac{7}{20}a+\frac{105}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-15q-\frac{7}{20}a+\frac{21}{4} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p-\frac{19}{2})(\frac{-12}{9}+b)& =(\color{red}{p}+\color{orange}{\frac{-19}{2}}).(\color{green}{b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{3}p-\frac{19}{2}b+\frac{19}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =bp-\frac{4}{3}p-\frac{19}{2}b+\frac{76}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{4}{3}p-\frac{19}{2}b+\frac{38}{3} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-15}{13}+b)(\frac{11}{2}+x)& =(\color{red}{b}+\color{orange}{\frac{-15}{13}}).(\color{green}{x}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{2}b-\frac{15}{13}x-\frac{15}{13}.\frac{11}{2}& \text{Uitwerken } \\ & =bx+\frac{11}{2}b-\frac{15}{13}x-\frac{165}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)