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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-13}{4}+b)(p-\frac{-8}{20})& =(\color{red}{b}+\color{orange}{\frac{-13}{4}}).(\color{green}{p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{5}b-\frac{13}{4}p-\frac{13}{4}.\frac{2}{5}& \text{Uitwerken } \\ & =bp+\frac{2}{5}b-\frac{13}{4}p-\frac{26}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{5}b-\frac{13}{4}p-\frac{13}{10} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{11}{16}+q)(x-(-11))& =(\color{red}{q}+\color{orange}{\frac{11}{16}}).(\color{green}{x}+\color{blue}{11})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(11)} + \color{orange}{(\frac{11}{16})} . \color{green}{(x)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = qx+11q+\frac{11}{16}x+\frac{11}{16}.11& \text{Uitwerken } \\ & =qx+11q+\frac{11}{16}x+\frac{121}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{13}{16})(\frac{13}{4}-b)& =(\color{red}{b}+\color{orange}{\frac{13}{16}}).(\color{green}{-b}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{13}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{13}{4}b-\frac{13}{16}b+\frac{13}{16}.\frac{13}{4}& \text{Uitwerken } \\ & =-b^2+(\frac{13}{4}+(\frac{-13}{16}))b+(\frac{-169}{64}) & \text{Neem samen} \\ &=-b^2+\frac{39}{16}b+(\frac{-169}{64}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{-12}{16}-q)(\frac{2}{2}-b)& =(\color{red}{-q}+\color{orange}{\frac{-3}{4}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq-1q+\frac{3}{4}b-\frac{3}{4}.1& \text{Uitwerken } \\ & =bq-1q+\frac{3}{4}b-\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{16}{5})(\frac{2}{7}+a)& =(\color{red}{b}+\color{orange}{\frac{-16}{5}}).(\color{green}{a}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{7}b-\frac{16}{5}a-\frac{16}{5}.\frac{2}{7}& \text{Uitwerken } \\ & =ab+\frac{2}{7}b-\frac{16}{5}a-\frac{32}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-\frac{-11}{7})(q-\frac{11}{11})& =(\color{red}{a}+\color{orange}{\frac{11}{7}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{11}{7})} . \color{green}{(q)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a+\frac{11}{7}q-\frac{11}{7}.1& \text{Uitwerken } \\ & =aq-1a+\frac{11}{7}q-\frac{11}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-4}{17}-x)(p-\frac{2}{15})& =(\color{red}{-x}+\color{orange}{\frac{-4}{17}}).(\color{green}{p}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(\frac{-4}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{15}x-\frac{4}{17}p+\frac{4}{17}.\frac{2}{15}& \text{Uitwerken } \\ & =-px+\frac{2}{15}x-\frac{4}{17}p+\frac{8}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-7}{20}-b)(q+\frac{-14}{11})& =(\color{red}{-b}+\color{orange}{\frac{-7}{20}}).(\color{green}{q}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{14}{11}b-\frac{7}{20}q+\frac{7}{20}.\frac{14}{11}& \text{Uitwerken } \\ & =-bq+\frac{14}{11}b-\frac{7}{20}q+\frac{98}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{14}{11}b-\frac{7}{20}q+\frac{49}{110} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q-\frac{5}{6})(a-\frac{-17}{10})& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{10}q-\frac{5}{6}a-\frac{5}{6}.\frac{17}{10}& \text{Uitwerken } \\ & =aq+\frac{17}{10}q-\frac{5}{6}a-\frac{85}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{17}{10}q-\frac{5}{6}a-\frac{17}{12} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p-\frac{15}{12})(\frac{-8}{9}+x)& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{x}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{8}{9}p-\frac{5}{4}x+\frac{5}{4}.\frac{8}{9}& \text{Uitwerken } \\ & =px-\frac{8}{9}p-\frac{5}{4}x+\frac{40}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{8}{9}p-\frac{5}{4}x+\frac{10}{9} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(a+\frac{-3}{8})(q+\frac{-12}{7})& =(\color{red}{a}+\color{orange}{\frac{-3}{8}}).(\color{green}{q}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{7})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{12}{7}a-\frac{3}{8}q+\frac{3}{8}.\frac{12}{7}& \text{Uitwerken } \\ & =aq-\frac{12}{7}a-\frac{3}{8}q+\frac{36}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{12}{7}a-\frac{3}{8}q+\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}((-3)-p)(\frac{17}{3}+p)& =(\color{red}{-p}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{17}{3}p-3p-3.\frac{17}{3}& \text{Uitwerken } \\ & =-p^2+((\frac{-17}{3})+(-3))p-\frac{51}{3} & \text{Neem samen} \\ &=-p^2-\frac{26}{3}p-\frac{51}{3} & \text{Maak de som} \\ &=-p^2-\frac{26}{3}p-17 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)