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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-\frac{-4}{10})((-14)+x)& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{(-14)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-14)} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = xx-14x+\frac{2}{5}x-\frac{2}{5}.14& \text{Uitwerken } \\ & =x^2+((-14)+\frac{2}{5})x-(\frac{-28}{5}) & \text{Neem samen} \\ &=x^2-\frac{68}{5}x-(\frac{-28}{5}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(a+\frac{3}{4})(\frac{20}{8}-q)& =(\color{red}{a}+\color{orange}{\frac{3}{4}}).(\color{green}{-q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{2}a-\frac{3}{4}q+\frac{3}{4}.\frac{5}{2}& \text{Uitwerken } \\ & =-aq+\frac{5}{2}a-\frac{3}{4}q+\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x+\frac{-11}{12})(\frac{-14}{4}-x)& =(\color{red}{x}+\color{orange}{\frac{-11}{12}}).(\color{green}{-x}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{7}{2}x+\frac{11}{12}x+\frac{11}{12}.\frac{7}{2}& \text{Uitwerken } \\ & =-x^2+((\frac{-7}{2})+\frac{11}{12})x+(\frac{-77}{24}) & \text{Neem samen} \\ &=-x^2-\frac{31}{12}x+(\frac{-77}{24}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(a+\frac{-12}{9})(\frac{18}{6}-b)& =(\color{red}{a}+\color{orange}{\frac{-4}{3}}).(\color{green}{-b}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -ab+3a+\frac{4}{3}b-\frac{4}{3}.3& \text{Uitwerken } \\ & =-ab+3a+\frac{4}{3}b-\frac{12}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+3a+\frac{4}{3}b-4 & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p+\frac{-11}{20})(x+\frac{-13}{6})& =(\color{red}{p}+\color{orange}{\frac{-11}{20}}).(\color{green}{x}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{6}p-\frac{11}{20}x+\frac{11}{20}.\frac{13}{6}& \text{Uitwerken } \\ & =px-\frac{13}{6}p-\frac{11}{20}x+\frac{143}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{5}{9})(a+\frac{-16}{3})& =(\color{red}{q}+\color{orange}{\frac{5}{9}}).(\color{green}{a}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{16}{3}q+\frac{5}{9}a-\frac{5}{9}.\frac{16}{3}& \text{Uitwerken } \\ & =aq-\frac{16}{3}q+\frac{5}{9}a-\frac{80}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q-\frac{-18}{10})(b+\frac{-17}{19})& =(\color{red}{q}+\color{orange}{\frac{9}{5}}).(\color{green}{b}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{9}{5})} . \color{green}{(b)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{19}q+\frac{9}{5}b-\frac{9}{5}.\frac{17}{19}& \text{Uitwerken } \\ & =bq-\frac{17}{19}q+\frac{9}{5}b-\frac{153}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-10}{13}-b)(\frac{10}{3}+a)& =(\color{red}{-b}+\color{orange}{\frac{-10}{13}}).(\color{green}{a}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{10}{3}b-\frac{10}{13}a-\frac{10}{13}.\frac{10}{3}& \text{Uitwerken } \\ & =-ab-\frac{10}{3}b-\frac{10}{13}a-\frac{100}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{16}{12}-a)(\frac{-17}{3}+b)& =(\color{red}{-a}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{17}{3}a+\frac{4}{3}b-\frac{4}{3}.\frac{17}{3}& \text{Uitwerken } \\ & =-ab+\frac{17}{3}a+\frac{4}{3}b-\frac{68}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-10}{4}-x)(b-\frac{-2}{8})& =(\color{red}{-x}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{4}x-\frac{5}{2}b-\frac{5}{2}.\frac{1}{4}& \text{Uitwerken } \\ & =-bx-\frac{1}{4}x-\frac{5}{2}b-\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{5}{6}-a)(p-\frac{-7}{5})& =(\color{red}{-a}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{5}a+\frac{5}{6}p+\frac{5}{6}.\frac{7}{5}& \text{Uitwerken } \\ & =-ap-\frac{7}{5}a+\frac{5}{6}p+\frac{35}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{7}{5}a+\frac{5}{6}p+\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-5}{9}+q)(\frac{3}{15}+x)& =(\color{red}{q}+\color{orange}{\frac{-5}{9}}).(\color{green}{x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{5}q-\frac{5}{9}x-\frac{5}{9}.\frac{1}{5}& \text{Uitwerken } \\ & =qx+\frac{1}{5}q-\frac{5}{9}x-\frac{5}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{5}q-\frac{5}{9}x-\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)