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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-(-20))(\frac{-2}{14}-b)& =(\color{red}{x}+\color{orange}{20}).(\color{green}{-b}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(20)} . \color{green}{(-b)} + \color{orange}{(20)} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{7}x-20b-20.\frac{1}{7}& \text{Uitwerken } \\ & =-bx-\frac{1}{7}x-20b-\frac{20}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a-\frac{-3}{18})(\frac{-20}{6}+p)& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{p}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{1}{6})} . \color{green}{(p)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{3}a+\frac{1}{6}p-\frac{1}{6}.\frac{10}{3}& \text{Uitwerken } \\ & =ap-\frac{10}{3}a+\frac{1}{6}p-\frac{10}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{10}{3}a+\frac{1}{6}p-\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}((-10)-p)(b+\frac{-13}{18})& =(\color{red}{-p}+\color{orange}{(-10)}).(\color{green}{b}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(-10)} . \color{green}{(b)} + \color{orange}{(-10)} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{18}p-10b+10.\frac{13}{18}& \text{Uitwerken } \\ & =-bp+\frac{13}{18}p-10b+\frac{130}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{13}{18}p-10b+\frac{65}{9} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(a+\frac{-17}{11})(\frac{1}{5}+b)& =(\color{red}{a}+\color{orange}{\frac{-17}{11}}).(\color{green}{b}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-17}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{5}a-\frac{17}{11}b-\frac{17}{11}.\frac{1}{5}& \text{Uitwerken } \\ & =ab+\frac{1}{5}a-\frac{17}{11}b-\frac{17}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-16}{18}+a)(p+\frac{19}{19})& =(\color{red}{a}+\color{orange}{\frac{-8}{9}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1a-\frac{8}{9}p-\frac{8}{9}.1& \text{Uitwerken } \\ & =ap+1a-\frac{8}{9}p-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-8}{12}-b)(p+\frac{6}{18})& =(\color{red}{-b}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{3}b-\frac{2}{3}p-\frac{2}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =-bp-\frac{1}{3}b-\frac{2}{3}p-\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b-\frac{4}{9})(\frac{18}{12}+x)& =(\color{red}{b}+\color{orange}{\frac{-4}{9}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{2}b-\frac{4}{9}x-\frac{4}{9}.\frac{3}{2}& \text{Uitwerken } \\ & =bx+\frac{3}{2}b-\frac{4}{9}x-\frac{12}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{2}b-\frac{4}{9}x-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-20}{16}+q)(a+\frac{7}{12})& =(\color{red}{q}+\color{orange}{\frac{-5}{4}}).(\color{green}{a}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{12}q-\frac{5}{4}a-\frac{5}{4}.\frac{7}{12}& \text{Uitwerken } \\ & =aq+\frac{7}{12}q-\frac{5}{4}a-\frac{35}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b+\frac{-17}{7})(a+\frac{20}{18})& =(\color{red}{b}+\color{orange}{\frac{-17}{7}}).(\color{green}{a}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-17}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{10}{9}b-\frac{17}{7}a-\frac{17}{7}.\frac{10}{9}& \text{Uitwerken } \\ & =ab+\frac{10}{9}b-\frac{17}{7}a-\frac{170}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-17}{13}-x)(\frac{-12}{13}+x)& =(\color{red}{-x}+\color{orange}{\frac{-17}{13}}).(\color{green}{x}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{-17}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{12}{13}x-\frac{17}{13}x+\frac{17}{13}.\frac{12}{13}& \text{Uitwerken } \\ & =-x^2+(\frac{12}{13}+(\frac{-17}{13}))x+(\frac{-204}{169}) & \text{Neem samen} \\ &=-x^2-\frac{5}{13}x+(\frac{-204}{169}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(b-\frac{4}{10})(\frac{-14}{20}-a)& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{-a}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{7}{10}b+\frac{2}{5}a+\frac{2}{5}.\frac{7}{10}& \text{Uitwerken } \\ & =-ab-\frac{7}{10}b+\frac{2}{5}a+\frac{14}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{7}{10}b+\frac{2}{5}a+\frac{7}{25} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-3}{4}+a)(2+p)& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2a-\frac{3}{4}p-\frac{3}{4}.2& \text{Uitwerken } \\ & =ap+2a-\frac{3}{4}p-\frac{6}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+2a-\frac{3}{4}p-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)