Question

$frac{a^{3}b^{3}-(cd)^{3}}{ab-cd}$ при a=$sqrt{6}$. b=$sqrt{8}$. c=$sqrt{6}$. d=$sqrt{2}$

Answer 1

$frac{(ab)^3-(cd)^3}{ab-cd}=frac{(ab-cd)((ab)^2+abcd+(cd)^2}{ab-cd}=(ab)^2+abcd+(cd)^2$

$(sqrt{6}sqrt{8})^2+sqrt{6}sqrt{8}sqrt{6}sqrt{2}+(sqrt{6}sqrt{2})^2 = 48+6*4+12 = 48+24+12 = 84$