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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-18}{17}+x)(q-\frac{-20}{8})& =(\color{red}{x}+\color{orange}{\frac{-18}{17}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{2}x-\frac{18}{17}q-\frac{18}{17}.\frac{5}{2}& \text{Uitwerken } \\ & =qx+\frac{5}{2}x-\frac{18}{17}q-\frac{90}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{5}{2}x-\frac{18}{17}q-\frac{45}{17} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p+\frac{-7}{4})(a+\frac{17}{12})& =(\color{red}{p}+\color{orange}{\frac{-7}{4}}).(\color{green}{a}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{12}p-\frac{7}{4}a-\frac{7}{4}.\frac{17}{12}& \text{Uitwerken } \\ & =ap+\frac{17}{12}p-\frac{7}{4}a-\frac{119}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-17}{11}+b)(11-p)& =(\color{red}{b}+\color{orange}{\frac{-17}{11}}).(\color{green}{-p}+\color{blue}{11})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(11)} + \color{orange}{(\frac{-17}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = -bp+11b+\frac{17}{11}p-\frac{17}{11}.11& \text{Uitwerken } \\ & =-bp+11b+\frac{17}{11}p-\frac{187}{11} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+11b+\frac{17}{11}p-17 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{19}{11}-b)(\frac{-12}{14}-a)& =(\color{red}{-b}+\color{orange}{\frac{19}{11}}).(\color{green}{-a}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{19}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{6}{7}b-\frac{19}{11}a-\frac{19}{11}.\frac{6}{7}& \text{Uitwerken } \\ & =ab+\frac{6}{7}b-\frac{19}{11}a-\frac{114}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{7}{7})(\frac{-16}{7}+a)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-16}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{7})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-16}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{16}{7}p+1a-1.\frac{16}{7}& \text{Uitwerken } \\ & =ap-\frac{16}{7}p+1a-\frac{16}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x-\frac{15}{20})(q+\frac{20}{17})& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{20}{17}x-\frac{3}{4}q-\frac{3}{4}.\frac{20}{17}& \text{Uitwerken } \\ & =qx+\frac{20}{17}x-\frac{3}{4}q-\frac{60}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{20}{17}x-\frac{3}{4}q-\frac{15}{17} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-14}{17}-q)(\frac{-17}{8}-b)& =(\color{red}{-q}+\color{orange}{\frac{-14}{17}}).(\color{green}{-b}+\color{blue}{\frac{-17}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{8})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{-17}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{8}q+\frac{14}{17}b+\frac{14}{17}.\frac{17}{8}& \text{Uitwerken } \\ & =bq+\frac{17}{8}q+\frac{14}{17}b+\frac{238}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{17}{8}q+\frac{14}{17}b+\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x+\frac{9}{19})(\frac{-17}{9}+x)& =(\color{red}{x}+\color{orange}{\frac{9}{19}}).(\color{green}{x}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(\frac{9}{19})} . \color{green}{(x)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{17}{9}x+\frac{9}{19}x-\frac{9}{19}.\frac{17}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-17}{9})+\frac{9}{19})x-(\frac{-153}{171}) & \text{Neem samen} \\ &=x^2-\frac{242}{171}x-(\frac{-153}{171}) & \text{Maak de som} \\ &=x^2-\frac{242}{171}x+\frac{17}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
9. \(\begin{align}(p+\frac{11}{13})(\frac{11}{6}-p)& =(\color{red}{p}+\color{orange}{\frac{11}{13}}).(\color{green}{-p}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{11}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{11}{6}p-\frac{11}{13}p+\frac{11}{13}.\frac{11}{6}& \text{Uitwerken } \\ & =-p^2+(\frac{11}{6}+(\frac{-11}{13}))p+(\frac{-121}{78}) & \text{Neem samen} \\ &=-p^2+\frac{77}{78}p+(\frac{-121}{78}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(p+\frac{-6}{5})(\frac{7}{4}+b)& =(\color{red}{p}+\color{orange}{\frac{-6}{5}}).(\color{green}{b}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{4}p-\frac{6}{5}b-\frac{6}{5}.\frac{7}{4}& \text{Uitwerken } \\ & =bp+\frac{7}{4}p-\frac{6}{5}b-\frac{42}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{7}{4}p-\frac{6}{5}b-\frac{21}{10} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{13}{10}+p)(\frac{18}{6}+q)& =(\color{red}{p}+\color{orange}{\frac{13}{10}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = pq+3p+\frac{13}{10}q+\frac{13}{10}.3& \text{Uitwerken } \\ & =pq+3p+\frac{13}{10}q+\frac{39}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{16}{19})(b+\frac{-8}{17})& =(\color{red}{x}+\color{orange}{\frac{-16}{19}}).(\color{green}{b}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{8}{17}x-\frac{16}{19}b+\frac{16}{19}.\frac{8}{17}& \text{Uitwerken } \\ & =bx-\frac{8}{17}x-\frac{16}{19}b+\frac{128}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)