Question

If x + y + z = 0, then find (x + y )^3+ (y + z )^3 +(z+x)^3.

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Answer 1

Answer:

Step-by-step explanation:

(x + y )^3+ (y + z )^3 +(z+x)^3= (x^3 + 3x^2y+ 3xy^2 + y^3 ) + (y^3 + 3y^2z+ 3yz^2 + z^3 ) +(z^3 + 3z^2x+ 3zx^2 + x^3 )

= (x^3+ y^3+ y^3+ z^3+z^3+x^3)+(3x^2y+ 3xy^2+3y^2z+ 3yz^2+3z^2x+ 3zx^2)

 =( 2 x^3+ 2  y^3+ 2 z^3) + (3x^2y+ 3xy^2+3y^2z+ 3yz^2+3z^2x+ 3zx^2)

=2(  x^3+  y^3+  z^3) + 3(x^2y+ xy^2+y^2z+ yz^2+z^2x+ zx^2)