Question

Phán tích thành nhân tử:

x³ + y³ + z³ - 3xyz

Answer 1

x​³ + y³ + z³ - 3xyz

= [ (x³+y³)+z³] -3xyz

=[ (x+y)³ +z³ ​+3xy (x+y) ] -3xyz

=[(x+y)³ +z³] +3x²y+3xy2​-3xyz

=(x+y+z)[(x+y)² -z(x+y)+z²] -3xy(x+y+z)

=(x+y+z) [x²​+2xy +y² - xz-yz +z² -3xy ]

=(x+y+z) (x²+y²+z² -xy-yz-zx)

Answer 2

x3 + y3 + z3 - 3xyz = (x + y)3 – 3x2y – 3xy2 + z3 – 3xyz

= (x + y)3 + z3 – 3x2y – 3xy2 - 3xyz 

= (x + y +z)[(x + y)2 – (x + y)z + z2)] - 3xy(x + y + z)

= (x + y + z)(x2 +2xy + y2 – xz – yz +z2 – 3xy)

= (x + y + z)(x2 + y2 +z2 – xy - yz – xz)