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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{4}{7})(\frac{-17}{14}+b)& =(\color{red}{q}+\color{orange}{\frac{-4}{7}}).(\color{green}{b}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{14}q-\frac{4}{7}b+\frac{4}{7}.\frac{17}{14}& \text{Uitwerken } \\ & =bq-\frac{17}{14}q-\frac{4}{7}b+\frac{68}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{17}{14}q-\frac{4}{7}b+\frac{34}{49} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{11}{12}-q)(q-\frac{-12}{19})& =(\color{red}{-q}+\color{orange}{\frac{11}{12}}).(\color{green}{q}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{11}{12})} . \color{green}{(q)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{12}{19}q+\frac{11}{12}q+\frac{11}{12}.\frac{12}{19}& \text{Uitwerken } \\ & =-q^2+((\frac{-12}{19})+\frac{11}{12})q+(\frac{-132}{228}) & \text{Neem samen} \\ &=-q^2+\frac{65}{228}q+(\frac{-132}{228}) & \text{Maak de som} \\ &=-q^2+\frac{65}{228}q+(\frac{-11}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
3. \(\begin{align}(p+\frac{4}{6})(b+\frac{5}{13})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{13}p+\frac{2}{3}b+\frac{2}{3}.\frac{5}{13}& \text{Uitwerken } \\ & =bp+\frac{5}{13}p+\frac{2}{3}b+\frac{10}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{2}{6})(x+\frac{-18}{8})& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{x}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{9}{4}x-\frac{1}{3}x+\frac{1}{3}.\frac{9}{4}& \text{Uitwerken } \\ & =x^2+((\frac{-9}{4})+(\frac{-1}{3}))x+\frac{9}{12} & \text{Neem samen} \\ &=x^2-\frac{31}{12}x+\frac{9}{12} & \text{Maak de som} \\ &=x^2-\frac{31}{12}x+\frac{3}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(q+\frac{-17}{19})(\frac{1}{16}+b)& =(\color{red}{q}+\color{orange}{\frac{-17}{19}}).(\color{green}{b}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{16}q-\frac{17}{19}b-\frac{17}{19}.\frac{1}{16}& \text{Uitwerken } \\ & =bq+\frac{1}{16}q-\frac{17}{19}b-\frac{17}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x-\frac{5}{4})(\frac{14}{8}-b)& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{-b}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{4}x+\frac{5}{4}b-\frac{5}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =-bx+\frac{7}{4}x+\frac{5}{4}b-\frac{35}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-19}{16}+b)(\frac{-11}{2}+p)& =(\color{red}{b}+\color{orange}{\frac{-19}{16}}).(\color{green}{p}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{2}b-\frac{19}{16}p+\frac{19}{16}.\frac{11}{2}& \text{Uitwerken } \\ & =bp-\frac{11}{2}b-\frac{19}{16}p+\frac{209}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a+\frac{14}{19})(a+\frac{15}{8})& =(\color{red}{a}+\color{orange}{\frac{14}{19}}).(\color{green}{a}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{14}{19})} . \color{green}{(a)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{15}{8}a+\frac{14}{19}a+\frac{14}{19}.\frac{15}{8}& \text{Uitwerken } \\ & =a^2+(\frac{15}{8}+\frac{14}{19})a+\frac{210}{152} & \text{Neem samen} \\ &=a^2+\frac{397}{152}a+\frac{210}{152} & \text{Maak de som} \\ &=a^2+\frac{397}{152}a+\frac{105}{76} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(b-\frac{-5}{13})(b-\frac{19}{11})& =(\color{red}{b}+\color{orange}{\frac{5}{13}}).(\color{green}{b}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{5}{13})} . \color{green}{(b)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{19}{11}b+\frac{5}{13}b-\frac{5}{13}.\frac{19}{11}& \text{Uitwerken } \\ & =b^2+((\frac{-19}{11})+\frac{5}{13})b-(\frac{-95}{143}) & \text{Neem samen} \\ &=b^2-\frac{192}{143}b-(\frac{-95}{143}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{-4}{15}+q)(q-\frac{-20}{10})& =(\color{red}{q}+\color{orange}{\frac{-4}{15}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{-4}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qq+2q-\frac{4}{15}q-\frac{4}{15}.2& \text{Uitwerken } \\ & =q^2+(2+(\frac{-4}{15}))q-(\frac{-8}{15}) & \text{Neem samen} \\ &=q^2+\frac{26}{15}q-(\frac{-8}{15}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(q+(-6))(\frac{-16}{19}-q)& =(\color{red}{q}+\color{orange}{(-6)}).(\color{green}{-q}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(-6)} . \color{green}{(-q)} + \color{orange}{(-6)} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{16}{19}q+6q+6.\frac{16}{19}& \text{Uitwerken } \\ & =-q^2+((\frac{-16}{19})+6)q+(\frac{-96}{19}) & \text{Neem samen} \\ &=-q^2+\frac{98}{19}q+(\frac{-96}{19}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{7}{5}+a)(\frac{-13}{2}-x)& =(\color{red}{a}+\color{orange}{\frac{7}{5}}).(\color{green}{-x}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{7}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{13}{2}a-\frac{7}{5}x-\frac{7}{5}.\frac{13}{2}& \text{Uitwerken } \\ & =-ax-\frac{13}{2}a-\frac{7}{5}x-\frac{91}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)