x ³+y ³+z ³ – 3xyz \giúp mình với/~( · ω ·) ~ 05/07/2021 Bởi Gabriella x ³+y ³+z ³ – 3xyz \giúp mình với/~( · ω ·) ~
$x^{3}$ + $y^{3}$ + $z^{3}$ – $3xyz$ =$(x+y)^{3}$ + $z^{3}$-3xy(x+y)-3xyz =(x+y+z)[($x+y)^{2}$ -(x+y)z +$z^{2}$]-3xy(x+y)-3xyz =(x+y+z)($x^{2}$ + 2xy + $y^{2}$ – xz -yz+$z^{2}$)-3xy(x+y+z) =(x+y+z)($x^{2}$ + 2xy +$y^{2}$ – xz -yz + $z^{2}$-3xy =(x+y+z)( $x^{2}$ +$y^{2}$+ $z^{2}$ -xy-xz-yz) Bình luận
$x^{3}$ + $y^{3}$ + $z^{3}$ – $3xyz$
=$(x+y)^{3}$ + $z^{3}$-3xy(x+y)-3xyz
=(x+y+z)[($x+y)^{2}$ -(x+y)z +$z^{2}$]-3xy(x+y)-3xyz
=(x+y+z)($x^{2}$ + 2xy + $y^{2}$ – xz -yz+$z^{2}$)-3xy(x+y+z)
=(x+y+z)($x^{2}$ + 2xy +$y^{2}$ – xz -yz + $z^{2}$-3xy
=(x+y+z)( $x^{2}$ +$y^{2}$+ $z^{2}$ -xy-xz-yz)