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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{16}{6}-b)(\frac{-8}{13}-x)& =(\color{red}{-b}+\color{orange}{\frac{8}{3}}).(\color{green}{-x}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{8}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{13}b-\frac{8}{3}x-\frac{8}{3}.\frac{8}{13}& \text{Uitwerken } \\ & =bx+\frac{8}{13}b-\frac{8}{3}x-\frac{64}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{6}{7})(a-\frac{-10}{4})& =(\color{red}{a}+\color{orange}{\frac{6}{7}}).(\color{green}{a}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{6}{7})} . \color{green}{(a)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{2}a+\frac{6}{7}a+\frac{6}{7}.\frac{5}{2}& \text{Uitwerken } \\ & =a^2+(\frac{5}{2}+\frac{6}{7})a+\frac{30}{14} & \text{Neem samen} \\ &=a^2+\frac{47}{14}a+\frac{30}{14} & \text{Maak de som} \\ &=a^2+\frac{47}{14}a+\frac{15}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
3. \(\begin{align}(\frac{5}{5}-q)(\frac{3}{15}-x)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{5}q-1x+1.\frac{1}{5}& \text{Uitwerken } \\ & =qx-\frac{1}{5}q-1x+\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{3}{6}+q)(\frac{-10}{6}+x)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{3}q+\frac{1}{2}x-\frac{1}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =qx-\frac{5}{3}q+\frac{1}{2}x-\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-14}{15}+b)(a+\frac{-18}{18})& =(\color{red}{b}+\color{orange}{\frac{-14}{15}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-14}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1b-\frac{14}{15}a+\frac{14}{15}.1& \text{Uitwerken } \\ & =ab-1b-\frac{14}{15}a+\frac{14}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-8}{8}-a)(b-(-20))& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{20})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(20)} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = -ab-20a-1b-1.20& \text{Uitwerken } \\ & =-ab-20a-1b-20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-8}{14}+p)(\frac{6}{8}+x)& =(\color{red}{p}+\color{orange}{\frac{-4}{7}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{4}p-\frac{4}{7}x-\frac{4}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =px+\frac{3}{4}p-\frac{4}{7}x-\frac{12}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{4}p-\frac{4}{7}x-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{18}{14}-b)(\frac{-11}{19}+a)& =(\color{red}{-b}+\color{orange}{\frac{9}{7}}).(\color{green}{a}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{9}{7})} . \color{green}{(a)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{11}{19}b+\frac{9}{7}a-\frac{9}{7}.\frac{11}{19}& \text{Uitwerken } \\ & =-ab+\frac{11}{19}b+\frac{9}{7}a-\frac{99}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{-20}{10})(\frac{10}{9}+a)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{10}{9}p+2a+2.\frac{10}{9}& \text{Uitwerken } \\ & =ap+\frac{10}{9}p+2a+\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x+(-7))(\frac{18}{7}+p)& =(\color{red}{x}+\color{orange}{(-7)}).(\color{green}{p}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(-7)} . \color{green}{(p)} + \color{orange}{(-7)} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{18}{7}x-7p-7.\frac{18}{7}& \text{Uitwerken } \\ & =px+\frac{18}{7}x-7p-\frac{126}{7} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{18}{7}x-7p-18 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p+\frac{7}{4})(\frac{-2}{18}-b)& =(\color{red}{p}+\color{orange}{\frac{7}{4}}).(\color{green}{-b}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{7}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{9}p-\frac{7}{4}b-\frac{7}{4}.\frac{1}{9}& \text{Uitwerken } \\ & =-bp-\frac{1}{9}p-\frac{7}{4}b-\frac{7}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{-16}{18})(b+\frac{-12}{7})& =(\color{red}{x}+\color{orange}{\frac{8}{9}}).(\color{green}{b}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{7})} + \color{orange}{(\frac{8}{9})} . \color{green}{(b)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{12}{7}x+\frac{8}{9}b-\frac{8}{9}.\frac{12}{7}& \text{Uitwerken } \\ & =bx-\frac{12}{7}x+\frac{8}{9}b-\frac{96}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{12}{7}x+\frac{8}{9}b-\frac{32}{21} & \text{Vereenvoudig} \\\end{align}\)