Question

Câu hỏi cho người học tốt nek

Câu 1: PT. ĐT. TNT

a) x^3+y^3-3xy+1

b) x^3+y^3+z^3-3xyz

Answer 1

Lời giải:
a. $x^3+y^3-3xy+1=(x+y)^3-3xy(x+y)-3xy+1$

$=(x+y)^3+1-[3xy(x+y)+3xy]$

$=(x+y+1)[(x+y)^2-(x+y)+1]-3xy(x+y+1)$

$=(x+y+1)(x^2+y^2+2xy-x-y+1-3xy)$

$=(x+y+1)(x^2+y^2-xy-x-y+1)$

b.

$x^3+y^3+z^3-3xyz=(x+y)^3-3xy(x+y)+z^3-3xyz$

$=[(x+y)^3+z^3]-3xy(x+y+z)$
$=(x+y+z)[(x+y)^2-z(x+y)+z^2]-3xy(x+y+z)$

$=(x+y+z)(x^2+y^2+z^2+2xy-xz-zy)-3xy(x+y+z)$
$=(x+y+z)(x^2+y^2+z^2+2xy-xz-zy-3xy)$

$=(x+y+z)(x^2+y^2+z^2-xy-xz-zy)