Giải thích các bước giải:
a) x(y+z)^2+y(x+z)^2+z(x+y)^2-4xyz=(x+z)(x+y)(y+z)
Đặt VT=x(y+z)^2+y(x+z)^2+z(x+y)^2-4xyz
=x.y²+x.z²+2xyz+y.x²+y.z²+2xyz+z.x²+z.y²+2xyz-4xyz
=x.y²+x.z²+2xyz+y.x²+y.z²+z.x²+z.y²
=(x.y²+x.yz)+(x.z²+xyz)+(y.x²+z.x²)+(z.y²+y.z²)
=xy.(y+z)+xz.(y+z)+x².(y+z)+yz.(y+z)
=(xy+yz+xz+x²).(y+z)
=(y+x).(x+z).(y+z)
⇒ đpcm
b)VT=a^2(b-c)+c^2(a-b)+b^2(c-a)
=a².b-a².c+c².a-c².b+b².c-b².a
VP=(a-c).(b-a).(c-b)
=(ab-a²-bc+ac).(c-b)
=abc-a.b²-a².c+a².b-b.c²+bv.c+a.c²-abc
=a².b-a².c+c².a-c².b+b².c-b².a
⇒VT=VP
⇒Đpcm
