A = \(\left(x^3+y^3\right)+\left(x^2z+y^2z-xyz\right)=\left(x+y\right)\left(x^2-xy+y^2\right)+z\left(x^2-xy+y^2\right)=\left(x^2-xy+y^2\right)\left(x+y+z\right)=\left(x^2-xy+y^2\right).0=0\)Kuroba Kaito = Kaito Kid :D

thanks

P = ...

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

\(\Leftrightarrow P=\left(x-z^2\right)\left[\left(x^2z-x^2y^2\right)+\left(y^3-yz\right)\right]\)

\(\Leftrightarrow P=\left(x-z^2\right)\left[-x^2\left(y^2-z\right)+y\left(y^2-z\right)\right]\)

\(\Leftrightarrow P=\left(x-z\right)^2\left(y^2-z\right)\left(y-x^2\right)\)

\(\Leftrightarrow P=abc\left(đpcm\right)\)

Sửa lại

P = ...

\(\Leftrightarrow P=...\)

\(\Leftrightarrow P=...-...+\left(xy^3-y^3z^2\right)+...\)

\(x+y+z=0\Rightarrow z=-\left(x+y\right)\)

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

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

\(=x^3+y^3-\left(x^3+y^3\right)=0\)

x+y+z=0⇒z=−(x+y)�+�+�=0⇒�=−(�+�)

x3+x2z+y2z−xyz+y3=x3+y3+(x2+y2−xy)z�3+�2�+�2�−���+�3=�3+�3+(�2+�2−��)�

=x3+y3−(x+y)(x2+y2−xy)=�3+�3−(�+�)(�2+�2−��)

=x3+y3−(x3+y3)=0