Ta có : ( x2 + y2)3 + ( z2 - x2)3
= ( y2 + z2)[ ( x2 + y2)2 - ( x2 + y2)( z2 - x2) + ( z2 - x2)2]
Thay vào A , ta có :
A = ( y2 + z2)[ ( x2 + y2)2 - ( x2 + y2)( z2 - x2) + ( z2 - x2)2 - ( y2 + z2)2]
A = ( y2 + z2)[ ( x2 + y2)( 2x2 + y2 - z2) + ( 2z2 - x2 + y2)(- y2 - x2)]
A = ( y2 + z2)[ ( x2 + y2)( 2x2 + y2 - z2 + x2 - 2z2 - y2)]
A= ( y2 + z2)( x2 + y2)( 3x2 - 3z2)
A = 3( y2 + z2)( x2 + y2)( x2 - z2)
\(\left(x^2+y^2\right)^3+\left(z^2-x^2\right)^3-\left[\left(x^2+y^2\right)+\left(z^2-x^2\right)\right]^3\\ =\left[\left(x^2+y^2\right)^3-\left(x^2+y^2\right)^3\right]+\left[\left(z^2-x^2\right)^3-\left(z^2-x^2\right)^3\right]-3\left(x^2+y^2\right)\left(z^2-x^2\right)\left(y^2+z^2\right)\\ =3\left(x^2+y^2\right)\left(x^2-z^2\right)\left(y^2+z^2\right)\\\)
