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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{7}{18}-q)(\frac{-18}{11}-p)& =(\color{red}{-q}+\color{orange}{\frac{7}{18}}).(\color{green}{-p}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{7}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{18}{11}q-\frac{7}{18}p-\frac{7}{18}.\frac{18}{11}& \text{Uitwerken } \\ & =pq+\frac{18}{11}q-\frac{7}{18}p-\frac{126}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{18}{11}q-\frac{7}{18}p-\frac{7}{11} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(19-p)(\frac{-20}{9}+b)& =(\color{red}{-p}+\color{orange}{19}).(\color{green}{b}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(19)} . \color{green}{(b)} + \color{orange}{(19)} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{20}{9}p+19b-19.\frac{20}{9}& \text{Uitwerken } \\ & =-bp+\frac{20}{9}p+19b-\frac{380}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a-\frac{-16}{12})(a+\frac{-17}{4})& =(\color{red}{a}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{17}{4}a+\frac{4}{3}a-\frac{4}{3}.\frac{17}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-17}{4})+\frac{4}{3})a-(\frac{-68}{12}) & \text{Neem samen} \\ &=a^2-\frac{35}{12}a-(\frac{-68}{12}) & \text{Maak de som} \\ &=a^2-\frac{35}{12}a+\frac{17}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
4. \(\begin{align}(p+7)(b+\frac{6}{6})& =(\color{red}{p}+\color{orange}{7}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(7)} . \color{green}{(b)} + \color{orange}{(7)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p+7b+7.1& \text{Uitwerken } \\ & =bp+1p+7b+7 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-2}{16}-a)(\frac{-2}{17}+p)& =(\color{red}{-a}+\color{orange}{\frac{-1}{8}}).(\color{green}{p}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{17}a-\frac{1}{8}p+\frac{1}{8}.\frac{2}{17}& \text{Uitwerken } \\ & =-ap+\frac{2}{17}a-\frac{1}{8}p+\frac{2}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{2}{17}a-\frac{1}{8}p+\frac{1}{68} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{4}{16}-p)(\frac{-13}{3}+b)& =(\color{red}{-p}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{3}p+\frac{1}{4}b-\frac{1}{4}.\frac{13}{3}& \text{Uitwerken } \\ & =-bp+\frac{13}{3}p+\frac{1}{4}b-\frac{13}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{3}{4}-b)(p-\frac{18}{3})& =(\color{red}{-b}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{(-6)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-6)} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -bp+6b+\frac{3}{4}p-\frac{3}{4}.6& \text{Uitwerken } \\ & =-bp+6b+\frac{3}{4}p-\frac{18}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+6b+\frac{3}{4}p-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x+\frac{-6}{11})(\frac{-6}{11}+p)& =(\color{red}{x}+\color{orange}{\frac{-6}{11}}).(\color{green}{p}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{6}{11}x-\frac{6}{11}p+\frac{6}{11}.\frac{6}{11}& \text{Uitwerken } \\ & =px-\frac{6}{11}x-\frac{6}{11}p+\frac{36}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b-\frac{-18}{11})(x+\frac{-13}{13})& =(\color{red}{b}+\color{orange}{\frac{18}{11}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{18}{11})} . \color{green}{(x)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx-1b+\frac{18}{11}x-\frac{18}{11}.1& \text{Uitwerken } \\ & =bx-1b+\frac{18}{11}x-\frac{18}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-9}{11}+p)(b+\frac{9}{19})& =(\color{red}{p}+\color{orange}{\frac{-9}{11}}).(\color{green}{b}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{19}p-\frac{9}{11}b-\frac{9}{11}.\frac{9}{19}& \text{Uitwerken } \\ & =bp+\frac{9}{19}p-\frac{9}{11}b-\frac{81}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-\frac{-12}{12})(\frac{-4}{15}+q)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{15}x+1q-1.\frac{4}{15}& \text{Uitwerken } \\ & =qx-\frac{4}{15}x+1q-\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{2}{20})(\frac{-10}{17}+x)& =(\color{red}{b}+\color{orange}{\frac{1}{10}}).(\color{green}{x}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{10}{17}b+\frac{1}{10}x-\frac{1}{10}.\frac{10}{17}& \text{Uitwerken } \\ & =bx-\frac{10}{17}b+\frac{1}{10}x-\frac{10}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{10}{17}b+\frac{1}{10}x-\frac{1}{17} & \text{Vereenvoudig} \\\end{align}\)