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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{10}{6}+a)(x+\frac{2}{5})& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{x}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{5}a+\frac{5}{3}x+\frac{5}{3}.\frac{2}{5}& \text{Uitwerken } \\ & =ax+\frac{2}{5}a+\frac{5}{3}x+\frac{10}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{5}a+\frac{5}{3}x+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(q-\frac{14}{13})(x+\frac{-7}{9})& =(\color{red}{q}+\color{orange}{\frac{-14}{13}}).(\color{green}{x}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{9}q-\frac{14}{13}x+\frac{14}{13}.\frac{7}{9}& \text{Uitwerken } \\ & =qx-\frac{7}{9}q-\frac{14}{13}x+\frac{98}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x+\frac{-5}{7})(\frac{-1}{15}+b)& =(\color{red}{x}+\color{orange}{\frac{-5}{7}}).(\color{green}{b}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{15}x-\frac{5}{7}b+\frac{5}{7}.\frac{1}{15}& \text{Uitwerken } \\ & =bx-\frac{1}{15}x-\frac{5}{7}b+\frac{5}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{15}x-\frac{5}{7}b+\frac{1}{21} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(x-\frac{-15}{16})(\frac{-5}{9}-x)& =(\color{red}{x}+\color{orange}{\frac{15}{16}}).(\color{green}{-x}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{15}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{5}{9}x-\frac{15}{16}x-\frac{15}{16}.\frac{5}{9}& \text{Uitwerken } \\ & =-x^2+((\frac{-5}{9})+(\frac{-15}{16}))x-\frac{75}{144} & \text{Neem samen} \\ &=-x^2-\frac{215}{144}x-\frac{75}{144} & \text{Maak de som} \\ &=-x^2-\frac{215}{144}x-\frac{25}{48} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(20-p)(\frac{3}{3}+q)& =(\color{red}{-p}+\color{orange}{20}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(20)} . \color{green}{(q)} + \color{orange}{(20)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pq-1p+20q+20.1& \text{Uitwerken } \\ & =-pq-1p+20q+20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p+\frac{12}{7})(a-\frac{12}{19})& =(\color{red}{p}+\color{orange}{\frac{12}{7}}).(\color{green}{a}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{12}{7})} . \color{green}{(a)} + \color{orange}{(\frac{12}{7})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{12}{19}p+\frac{12}{7}a-\frac{12}{7}.\frac{12}{19}& \text{Uitwerken } \\ & =ap-\frac{12}{19}p+\frac{12}{7}a-\frac{144}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{-8}{16})(\frac{16}{19}+x)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{16}{19}b-\frac{1}{2}x-\frac{1}{2}.\frac{16}{19}& \text{Uitwerken } \\ & =bx+\frac{16}{19}b-\frac{1}{2}x-\frac{16}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{16}{19}b-\frac{1}{2}x-\frac{8}{19} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{7}{19}+a)(b+\frac{13}{6})& =(\color{red}{a}+\color{orange}{\frac{7}{19}}).(\color{green}{b}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{7}{19})} . \color{green}{(b)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{6}a+\frac{7}{19}b+\frac{7}{19}.\frac{13}{6}& \text{Uitwerken } \\ & =ab+\frac{13}{6}a+\frac{7}{19}b+\frac{91}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-20}{2}-b)(\frac{16}{3}-x)& =(\color{red}{-b}+\color{orange}{(-10)}).(\color{green}{-x}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(-10)} . \color{green}{(-x)} + \color{orange}{(-10)} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{16}{3}b+10x-10.\frac{16}{3}& \text{Uitwerken } \\ & =bx-\frac{16}{3}b+10x-\frac{160}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{5}{20}+a)(\frac{11}{20}+x)& =(\color{red}{a}+\color{orange}{\frac{1}{4}}).(\color{green}{x}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{20}a+\frac{1}{4}x+\frac{1}{4}.\frac{11}{20}& \text{Uitwerken } \\ & =ax+\frac{11}{20}a+\frac{1}{4}x+\frac{11}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{-15}{13})(p+\frac{8}{17})& =(\color{red}{q}+\color{orange}{\frac{15}{13}}).(\color{green}{p}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{15}{13})} . \color{green}{(p)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{17}q+\frac{15}{13}p+\frac{15}{13}.\frac{8}{17}& \text{Uitwerken } \\ & =pq+\frac{8}{17}q+\frac{15}{13}p+\frac{120}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b-\frac{-3}{17})(\frac{-2}{5}+a)& =(\color{red}{b}+\color{orange}{\frac{3}{17}}).(\color{green}{a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{3}{17})} . \color{green}{(a)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{5}b+\frac{3}{17}a-\frac{3}{17}.\frac{2}{5}& \text{Uitwerken } \\ & =ab-\frac{2}{5}b+\frac{3}{17}a-\frac{6}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)