If x+y+z=0, then find (x+y)³ + (y+z)³ + (z+x)³.
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Given, x + y + z = 0
⇒2(x + y + z) = 2.0 = 0
⇒ (x + y) + (y + z ) + (z + x) = 0
Let (x + y) = A , (y + z) = B and (z + x) = C
Then, A + B + C = 0
But we know, if A + B + C = 0, then, A³ + B³ + C³ = 3ABC
Now, put A, B and C values from above ,
⇒(x + y)³ + (y + z)³ + (z + x)³ = 3(x + y)(y + z)(z + x)
Hence, answer is 3(x + y)(y + z)(z + x)
⇒2(x + y + z) = 2.0 = 0
⇒ (x + y) + (y + z ) + (z + x) = 0
Let (x + y) = A , (y + z) = B and (z + x) = C
Then, A + B + C = 0
But we know, if A + B + C = 0, then, A³ + B³ + C³ = 3ABC
Now, put A, B and C values from above ,
⇒(x + y)³ + (y + z)³ + (z + x)³ = 3(x + y)(y + z)(z + x)
Hence, answer is 3(x + y)(y + z)(z + x)
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