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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{-6}{2})(b-\frac{11}{7})& =(\color{red}{b}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{11}{7}b+3b-3.\frac{11}{7}& \text{Uitwerken } \\ & =b^2+((\frac{-11}{7})+3)b-(\frac{-33}{7}) & \text{Neem samen} \\ &=b^2+\frac{10}{7}b-(\frac{-33}{7}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(x+\frac{-5}{8})(x+\frac{-8}{16})& =(\color{red}{x}+\color{orange}{\frac{-5}{8}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{2}x-\frac{5}{8}x+\frac{5}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{2})+(\frac{-5}{8}))x+\frac{5}{16} & \text{Neem samen} \\ &=x^2-\frac{9}{8}x+\frac{5}{16} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(x+\frac{-20}{8})(\frac{3}{2}-b)& =(\color{red}{x}+\color{orange}{\frac{-5}{2}}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{2}x+\frac{5}{2}b-\frac{5}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =-bx+\frac{3}{2}x+\frac{5}{2}b-\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{6}{14})(\frac{11}{14}-x)& =(\color{red}{x}+\color{orange}{\frac{-3}{7}}).(\color{green}{-x}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{11}{14}x+\frac{3}{7}x-\frac{3}{7}.\frac{11}{14}& \text{Uitwerken } \\ & =-x^2+(\frac{11}{14}+\frac{3}{7})x-\frac{33}{98} & \text{Neem samen} \\ &=-x^2+\frac{17}{14}x-\frac{33}{98} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(a+\frac{10}{2})(\frac{-13}{15}-p)& =(\color{red}{a}+\color{orange}{5}).(\color{green}{-p}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(5)} . \color{green}{(-p)} + \color{orange}{(5)} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{15}a-5p-5.\frac{13}{15}& \text{Uitwerken } \\ & =-ap-\frac{13}{15}a-5p-\frac{65}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{13}{15}a-5p-\frac{13}{3} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{5}{4}-x)(b+\frac{-12}{13})& =(\color{red}{-x}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{12}{13}x+\frac{5}{4}b-\frac{5}{4}.\frac{12}{13}& \text{Uitwerken } \\ & =-bx+\frac{12}{13}x+\frac{5}{4}b-\frac{60}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{12}{13}x+\frac{5}{4}b-\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-20}{14}-x)(x-\frac{13}{8})& =(\color{red}{-x}+\color{orange}{\frac{-10}{7}}).(\color{green}{x}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{13}{8}x-\frac{10}{7}x+\frac{10}{7}.\frac{13}{8}& \text{Uitwerken } \\ & =-x^2+(\frac{13}{8}+(\frac{-10}{7}))x+(\frac{-130}{56}) & \text{Neem samen} \\ &=-x^2+\frac{11}{56}x+(\frac{-130}{56}) & \text{Maak de som} \\ &=-x^2+\frac{11}{56}x+(\frac{-65}{28}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(b+\frac{-6}{9})(a+\frac{11}{2})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{2}b-\frac{2}{3}a-\frac{2}{3}.\frac{11}{2}& \text{Uitwerken } \\ & =ab+\frac{11}{2}b-\frac{2}{3}a-\frac{22}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{11}{2}b-\frac{2}{3}a-\frac{11}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q+\frac{14}{7})(p+(-18))& =(\color{red}{q}+\color{orange}{2}).(\color{green}{p}+\color{blue}{(-18)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-18)} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = pq-18q+2p-2.18& \text{Uitwerken } \\ & =pq-18q+2p-36 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{10}{13}+q)((-9)+x)& =(\color{red}{q}+\color{orange}{\frac{10}{13}}).(\color{green}{x}+\color{blue}{(-9)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-9)} + \color{orange}{(\frac{10}{13})} . \color{green}{(x)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = qx-9q+\frac{10}{13}x-\frac{10}{13}.9& \text{Uitwerken } \\ & =qx-9q+\frac{10}{13}x-\frac{90}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-7}{8}+b)(\frac{7}{19}-x)& =(\color{red}{b}+\color{orange}{\frac{-7}{8}}).(\color{green}{-x}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{19}b+\frac{7}{8}x-\frac{7}{8}.\frac{7}{19}& \text{Uitwerken } \\ & =-bx+\frac{7}{19}b+\frac{7}{8}x-\frac{49}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-5}{2}+a)(b-\frac{4}{5})& =(\color{red}{a}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{5}a-\frac{5}{2}b+\frac{5}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =ab-\frac{4}{5}a-\frac{5}{2}b+\frac{20}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{4}{5}a-\frac{5}{2}b+2 & \text{Vereenvoudig} \\\end{align}\)