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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}((-9)-a)(x+\frac{-7}{13})& =(\color{red}{-a}+\color{orange}{(-9)}).(\color{green}{x}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(-9)} . \color{green}{(x)} + \color{orange}{(-9)} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{13}a-9x+9.\frac{7}{13}& \text{Uitwerken } \\ & =-ax+\frac{7}{13}a-9x+\frac{63}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-9}{12}-a)(p+\frac{-5}{3})& =(\color{red}{-a}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{3}a-\frac{3}{4}p+\frac{3}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =-ap+\frac{5}{3}a-\frac{3}{4}p+\frac{15}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{5}{3}a-\frac{3}{4}p+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b-\frac{-16}{4})(\frac{9}{8}+x)& =(\color{red}{b}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{8}b+4x+4.\frac{9}{8}& \text{Uitwerken } \\ & =bx+\frac{9}{8}b+4x+\frac{36}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{9}{8}b+4x+\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b+\frac{-5}{9})(q-9)& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{q}+\color{blue}{(-9)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-9)} + \color{orange}{(\frac{-5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = bq-9b-\frac{5}{9}q+\frac{5}{9}.9& \text{Uitwerken } \\ & =bq-9b-\frac{5}{9}q+\frac{45}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-9b-\frac{5}{9}q+5 & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-20}{18}-b)(x-\frac{20}{5})& =(\color{red}{-b}+\color{orange}{\frac{-10}{9}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(-4)} + \color{orange}{(\frac{-10}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -bx+4b-\frac{10}{9}x+\frac{10}{9}.4& \text{Uitwerken } \\ & =-bx+4b-\frac{10}{9}x+\frac{40}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-19}{9}-q)(q-\frac{-13}{20})& =(\color{red}{-q}+\color{orange}{\frac{-19}{9}}).(\color{green}{q}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{13}{20}q-\frac{19}{9}q-\frac{19}{9}.\frac{13}{20}& \text{Uitwerken } \\ & =-q^2+((\frac{-13}{20})+(\frac{-19}{9}))q-\frac{247}{180} & \text{Neem samen} \\ &=-q^2-\frac{497}{180}q-\frac{247}{180} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(x-\frac{8}{6})(q+\frac{6}{13})& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{6}{13}x-\frac{4}{3}q-\frac{4}{3}.\frac{6}{13}& \text{Uitwerken } \\ & =qx+\frac{6}{13}x-\frac{4}{3}q-\frac{24}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{6}{13}x-\frac{4}{3}q-\frac{8}{13} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-15}{20}+p)(5-a)& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{-a}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(5)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -ap+5p+\frac{3}{4}a-\frac{3}{4}.5& \text{Uitwerken } \\ & =-ap+5p+\frac{3}{4}a-\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{-5}{18})(\frac{5}{15}-b)& =(\color{red}{x}+\color{orange}{\frac{5}{18}}).(\color{green}{-b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{5}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{3}x-\frac{5}{18}b+\frac{5}{18}.\frac{1}{3}& \text{Uitwerken } \\ & =-bx+\frac{1}{3}x-\frac{5}{18}b+\frac{5}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{6}{5})(\frac{-1}{9}+p)& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{9}a+\frac{6}{5}p-\frac{6}{5}.\frac{1}{9}& \text{Uitwerken } \\ & =ap-\frac{1}{9}a+\frac{6}{5}p-\frac{6}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{1}{9}a+\frac{6}{5}p-\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q-\frac{-16}{17})(q+\frac{-18}{15})& =(\color{red}{q}+\color{orange}{\frac{16}{17}}).(\color{green}{q}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{16}{17})} . \color{green}{(q)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{6}{5}q+\frac{16}{17}q-\frac{16}{17}.\frac{6}{5}& \text{Uitwerken } \\ & =q^2+((\frac{-6}{5})+\frac{16}{17})q-(\frac{-96}{85}) & \text{Neem samen} \\ &=q^2-\frac{22}{85}q-(\frac{-96}{85}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{13}{13}+x)(\frac{4}{14}+a)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{7}x+1a+1.\frac{2}{7}& \text{Uitwerken } \\ & =ax+\frac{2}{7}x+1a+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)