Question

Phân tich thanh nhân tư băng cach dung hăng đăng thưc:

           x³ + y³ +z³ -3xyz

       Help me.....Thanks!!!!

Answer 1

x³+3x²y+3xy²+y³+z³-3x²y-3xy²-3xyz

= (x+y)³+z³-3xy(x+y+z)

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

=(x+y+z)(x²+y²+z²-xy-yz-xz) 

Đó là cách của mình

Answer 2

Ta có: \(x^3+y^3+z^3-3xyz\)

= \(\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\)

=\(\left(\left(x+y\right)^3+z^3\right)-3xy\left(x+y+z\right)\)

= \(\left(x+y+z\right)\left(\left(x+y\right)^2-\left(x+y\right)z+z^2\right)-3xy\left(x+y+z\right)\)

= \(\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2-3xy\right)\)

= \(\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)