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

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

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Verbetersleutel

1. \(\begin{align}(p-\frac{-3}{16})(\frac{-6}{15}+b)& =(\color{red}{p}+\color{orange}{\frac{3}{16}}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{3}{16})} . \color{green}{(b)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{5}p+\frac{3}{16}b-\frac{3}{16}.\frac{2}{5}& \text{Uitwerken } \\ & =bp-\frac{2}{5}p+\frac{3}{16}b-\frac{6}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{2}{5}p+\frac{3}{16}b-\frac{3}{40} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{11}{12}+a)(\frac{11}{7}-x)& =(\color{red}{a}+\color{orange}{\frac{11}{12}}).(\color{green}{-x}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(\frac{11}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{11}{7}a-\frac{11}{12}x+\frac{11}{12}.\frac{11}{7}& \text{Uitwerken } \\ & =-ax+\frac{11}{7}a-\frac{11}{12}x+\frac{121}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a+\frac{12}{12})(p-\frac{7}{17})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{17}a+1p-1.\frac{7}{17}& \text{Uitwerken } \\ & =ap-\frac{7}{17}a+1p-\frac{7}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{16}{17}-x)(\frac{18}{12}-a)& =(\color{red}{-x}+\color{orange}{\frac{16}{17}}).(\color{green}{-a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{16}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{2}x-\frac{16}{17}a+\frac{16}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =ax-\frac{3}{2}x-\frac{16}{17}a+\frac{48}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{3}{2}x-\frac{16}{17}a+\frac{24}{17} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x+\frac{20}{14})(\frac{-14}{15}-p)& =(\color{red}{x}+\color{orange}{\frac{10}{7}}).(\color{green}{-p}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{14}{15}x-\frac{10}{7}p-\frac{10}{7}.\frac{14}{15}& \text{Uitwerken } \\ & =-px-\frac{14}{15}x-\frac{10}{7}p-\frac{140}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{14}{15}x-\frac{10}{7}p-\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-7}{7}+q)(a-\frac{18}{12})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{2}q-1a+1.\frac{3}{2}& \text{Uitwerken } \\ & =aq-\frac{3}{2}q-1a+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-18}{7}+q)(\frac{-8}{17}-a)& =(\color{red}{q}+\color{orange}{\frac{-18}{7}}).(\color{green}{-a}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{8}{17}q+\frac{18}{7}a+\frac{18}{7}.\frac{8}{17}& \text{Uitwerken } \\ & =-aq-\frac{8}{17}q+\frac{18}{7}a+\frac{144}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-18}{14}-b)(q+\frac{11}{15})& =(\color{red}{-b}+\color{orange}{\frac{-9}{7}}).(\color{green}{q}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{15}b-\frac{9}{7}q-\frac{9}{7}.\frac{11}{15}& \text{Uitwerken } \\ & =-bq-\frac{11}{15}b-\frac{9}{7}q-\frac{99}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{11}{15}b-\frac{9}{7}q-\frac{33}{35} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{8}{3}-x)(q+\frac{-13}{2})& =(\color{red}{-x}+\color{orange}{\frac{8}{3}}).(\color{green}{q}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{2}x+\frac{8}{3}q-\frac{8}{3}.\frac{13}{2}& \text{Uitwerken } \\ & =-qx+\frac{13}{2}x+\frac{8}{3}q-\frac{104}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{13}{2}x+\frac{8}{3}q-\frac{52}{3} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-5}{19}-q)(b-\frac{18}{16})& =(\color{red}{-q}+\color{orange}{\frac{-5}{19}}).(\color{green}{b}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{9}{8}q-\frac{5}{19}b+\frac{5}{19}.\frac{9}{8}& \text{Uitwerken } \\ & =-bq+\frac{9}{8}q-\frac{5}{19}b+\frac{45}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{18}{11})(\frac{13}{20}+q)& =(\color{red}{x}+\color{orange}{\frac{18}{11}}).(\color{green}{q}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{18}{11})} . \color{green}{(q)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{20}x+\frac{18}{11}q+\frac{18}{11}.\frac{13}{20}& \text{Uitwerken } \\ & =qx+\frac{13}{20}x+\frac{18}{11}q+\frac{234}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{13}{20}x+\frac{18}{11}q+\frac{117}{110} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(a+\frac{-4}{12})(b-\frac{18}{10})& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{5}a-\frac{1}{3}b+\frac{1}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =ab-\frac{9}{5}a-\frac{1}{3}b+\frac{9}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{9}{5}a-\frac{1}{3}b+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)