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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{3}{13}-p)(q-\frac{6}{9})& =(\color{red}{-p}+\color{orange}{\frac{3}{13}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{3}{13})} . \color{green}{(q)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{2}{3}p+\frac{3}{13}q-\frac{3}{13}.\frac{2}{3}& \text{Uitwerken } \\ & =-pq+\frac{2}{3}p+\frac{3}{13}q-\frac{6}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{2}{3}p+\frac{3}{13}q-\frac{2}{13} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{3}{18}-p)(a+\frac{-5}{2})& =(\color{red}{-p}+\color{orange}{\frac{1}{6}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{2}p+\frac{1}{6}a-\frac{1}{6}.\frac{5}{2}& \text{Uitwerken } \\ & =-ap+\frac{5}{2}p+\frac{1}{6}a-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a+\frac{-8}{3})(\frac{-18}{16}-p)& =(\color{red}{a}+\color{orange}{\frac{-8}{3}}).(\color{green}{-p}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{8}a+\frac{8}{3}p+\frac{8}{3}.\frac{9}{8}& \text{Uitwerken } \\ & =-ap-\frac{9}{8}a+\frac{8}{3}p+\frac{72}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{9}{8}a+\frac{8}{3}p+3 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p+\frac{13}{15})(x+\frac{-18}{17})& =(\color{red}{p}+\color{orange}{\frac{13}{15}}).(\color{green}{x}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{13}{15})} . \color{green}{(x)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{18}{17}p+\frac{13}{15}x-\frac{13}{15}.\frac{18}{17}& \text{Uitwerken } \\ & =px-\frac{18}{17}p+\frac{13}{15}x-\frac{234}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{18}{17}p+\frac{13}{15}x-\frac{78}{85} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(b+\frac{-10}{13})(\frac{4}{6}-x)& =(\color{red}{b}+\color{orange}{\frac{-10}{13}}).(\color{green}{-x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{2}{3}b+\frac{10}{13}x-\frac{10}{13}.\frac{2}{3}& \text{Uitwerken } \\ & =-bx+\frac{2}{3}b+\frac{10}{13}x-\frac{20}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-\frac{-13}{13})(a+\frac{-1}{20})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{20}a+1a-1.\frac{1}{20}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{20})+1)a-(\frac{-1}{20}) & \text{Neem samen} \\ &=a^2+\frac{19}{20}a-(\frac{-1}{20}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{15}{7}-a)(p-\frac{2}{2})& =(\color{red}{-a}+\color{orange}{\frac{15}{7}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(-1)} + \color{orange}{(\frac{15}{7})} . \color{green}{(p)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1a+\frac{15}{7}p-\frac{15}{7}.1& \text{Uitwerken } \\ & =-ap+1a+\frac{15}{7}p-\frac{15}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-17}{15}+x)(\frac{14}{7}+x)& =(\color{red}{x}+\color{orange}{\frac{-17}{15}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = xx+2x-\frac{17}{15}x-\frac{17}{15}.2& \text{Uitwerken } \\ & =x^2+(2+(\frac{-17}{15}))x-(\frac{-34}{15}) & \text{Neem samen} \\ &=x^2+\frac{13}{15}x-(\frac{-34}{15}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(x-\frac{6}{3})(\frac{5}{10}-b)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{-b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-2)} . \color{green}{(-b)} + \color{orange}{(-2)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{2}x+2b-2.\frac{1}{2}& \text{Uitwerken } \\ & =-bx+\frac{1}{2}x+2b-\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{1}{2}x+2b-1 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(x-\frac{18}{16})(q-\frac{-16}{10})& =(\color{red}{x}+\color{orange}{\frac{-9}{8}}).(\color{green}{q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{8}{5}x-\frac{9}{8}q-\frac{9}{8}.\frac{8}{5}& \text{Uitwerken } \\ & =qx+\frac{8}{5}x-\frac{9}{8}q-\frac{72}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{8}{5}x-\frac{9}{8}q-\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-14}{17}+b)(b+\frac{4}{13})& =(\color{red}{b}+\color{orange}{\frac{-14}{17}}).(\color{green}{b}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{4}{13}b-\frac{14}{17}b-\frac{14}{17}.\frac{4}{13}& \text{Uitwerken } \\ & =b^2+(\frac{4}{13}+(\frac{-14}{17}))b-(\frac{-56}{221}) & \text{Neem samen} \\ &=b^2-\frac{114}{221}b-(\frac{-56}{221}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{11}{8}+a)(q+\frac{2}{5})& =(\color{red}{a}+\color{orange}{\frac{11}{8}}).(\color{green}{q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{11}{8})} . \color{green}{(q)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{5}a+\frac{11}{8}q+\frac{11}{8}.\frac{2}{5}& \text{Uitwerken } \\ & =aq+\frac{2}{5}a+\frac{11}{8}q+\frac{22}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{2}{5}a+\frac{11}{8}q+\frac{11}{20} & \text{Vereenvoudig} \\\end{align}\)