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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{6}{15})(q-\frac{5}{9})& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{q}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{9}x+\frac{2}{5}q-\frac{2}{5}.\frac{5}{9}& \text{Uitwerken } \\ & =qx-\frac{5}{9}x+\frac{2}{5}q-\frac{10}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{9}x+\frac{2}{5}q-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(a+\frac{3}{13})(\frac{-20}{15}-x)& =(\color{red}{a}+\color{orange}{\frac{3}{13}}).(\color{green}{-x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{3}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{4}{3}a-\frac{3}{13}x-\frac{3}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =-ax-\frac{4}{3}a-\frac{3}{13}x-\frac{12}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{4}{3}a-\frac{3}{13}x-\frac{4}{13} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-20}{12}-x)(b-\frac{3}{4})& =(\color{red}{-x}+\color{orange}{\frac{-5}{3}}).(\color{green}{b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{4}x-\frac{5}{3}b+\frac{5}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =-bx+\frac{3}{4}x-\frac{5}{3}b+\frac{15}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{3}{4}x-\frac{5}{3}b+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{16}{8}+p)(\frac{-11}{14}+q)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{14}p+2q-2.\frac{11}{14}& \text{Uitwerken } \\ & =pq-\frac{11}{14}p+2q-\frac{22}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{11}{14}p+2q-\frac{11}{7} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p-\frac{-20}{7})(\frac{-9}{6}+a)& =(\color{red}{p}+\color{orange}{\frac{20}{7}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{20}{7})} . \color{green}{(a)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{2}p+\frac{20}{7}a-\frac{20}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =ap-\frac{3}{2}p+\frac{20}{7}a-\frac{60}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{3}{2}p+\frac{20}{7}a-\frac{30}{7} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{13}{12}-x)(a+\frac{-8}{14})& =(\color{red}{-x}+\color{orange}{\frac{13}{12}}).(\color{green}{a}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{13}{12})} . \color{green}{(a)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{7}x+\frac{13}{12}a-\frac{13}{12}.\frac{4}{7}& \text{Uitwerken } \\ & =-ax+\frac{4}{7}x+\frac{13}{12}a-\frac{52}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{4}{7}x+\frac{13}{12}a-\frac{13}{21} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-20}{12}+b)(\frac{-9}{14}-a)& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{-a}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{9}{14}b+\frac{5}{3}a+\frac{5}{3}.\frac{9}{14}& \text{Uitwerken } \\ & =-ab-\frac{9}{14}b+\frac{5}{3}a+\frac{45}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{9}{14}b+\frac{5}{3}a+\frac{15}{14} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{20}{14}+b)(b-\frac{-20}{8})& =(\color{red}{b}+\color{orange}{\frac{10}{7}}).(\color{green}{b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{2}b+\frac{10}{7}b+\frac{10}{7}.\frac{5}{2}& \text{Uitwerken } \\ & =b^2+(\frac{5}{2}+\frac{10}{7})b+\frac{50}{14} & \text{Neem samen} \\ &=b^2+\frac{55}{14}b+\frac{50}{14} & \text{Maak de som} \\ &=b^2+\frac{55}{14}b+\frac{25}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(p+\frac{-18}{12})(q-\frac{-20}{20})& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p-\frac{3}{2}q-\frac{3}{2}.1& \text{Uitwerken } \\ & =pq+1p-\frac{3}{2}q-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-15}{8})(b-\frac{-16}{17})& =(\color{red}{x}+\color{orange}{\frac{15}{8}}).(\color{green}{b}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{15}{8})} . \color{green}{(b)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{16}{17}x+\frac{15}{8}b+\frac{15}{8}.\frac{16}{17}& \text{Uitwerken } \\ & =bx+\frac{16}{17}x+\frac{15}{8}b+\frac{240}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{16}{17}x+\frac{15}{8}b+\frac{30}{17} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{11}{16}+a)(x-\frac{-20}{16})& =(\color{red}{a}+\color{orange}{\frac{11}{16}}).(\color{green}{x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{11}{16})} . \color{green}{(x)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{4}a+\frac{11}{16}x+\frac{11}{16}.\frac{5}{4}& \text{Uitwerken } \\ & =ax+\frac{5}{4}a+\frac{11}{16}x+\frac{55}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{-17}{11})(b-\frac{-5}{4})& =(\color{red}{x}+\color{orange}{\frac{17}{11}}).(\color{green}{b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{17}{11})} . \color{green}{(b)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{4}x+\frac{17}{11}b+\frac{17}{11}.\frac{5}{4}& \text{Uitwerken } \\ & =bx+\frac{5}{4}x+\frac{17}{11}b+\frac{85}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)