Question

Simplify (x³-y³)³+(y³-z³)³+(z³-x³)³%(x-y)³+(y-z)³+(z-x)³

Answer 1

Answer:

(x² + y² + xy)(y² + z² + yz)(z² + x² + xz)

Step-by-step explanation:

Simplify (x³-y³)³+(y³-z³)³+(z³-x³)³/ (x-y)³+(y-z)³+(z-x)³

if a + b + c = 0  then a³ + b³ + c³ = 3abc

In Numerator

 a = x³-y³ , b = y³-z³  & c = z³-x³

=> a + b + c = x³-y³ + y³-z³ + z³-x³ = 0

=> numerator = 3(x³-y³)(y³-z³)( z³-x³)

in Denominator

 a = x-y , b = y-z  & c = z-x

=> a + b + c = x-y + y-z + z-x = 0

=> numerator = 3(x-y)(y-z)( z-x)

(x³-y³)³+(y³-z³)³+(z³-x³)³/ (x-y)³+(y-z)³+(z-x)³

=  3(x³-y³)(y³-z³)( z³-x³)/3(x-y)(y-z)( z-x)

=  (x³-y³)(y³-z³)( z³-x³)/(x-y)(y-z)( z-x)

(a³ - b³)/(a-b) = a² + b² + ab

= (x² + y² + xy)(y² + z² + yz)(z² + x² + xz)