Question

Factorize:
(3x-2y)³+(2y-4z)³+(4z-3x)³

Answer 1

Answer:

Given Equation is (3x - 2y)^3 + (2y - 4z)^3 + (4z - 3x)^3

We know that (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3

= > 27x^3 - 54x^2y + 36xy^2 - 8y^3 + 8y^3 - 48y^2z + 96yz^2 - 64z^3 + 64z^3 - 144xz^2 + 108x^2z - 27x^3

= > -54x^2y + 108x^2z + 36xy^2 - 144xz^2 - 48y^2z + 96yz^2.

= > -6(9x^2y - 18x^2z - 6xy^2 + 24xz^2 + 8y^2z - 16yz^2)

= > -6(9x^2y - 18x^2z - 12xyz + 12xyz + 24xz^2 - 6xy^2 + 8y^2z - 16yz^2)

= > -6(9x^2y - 18x^2z - 12xyz + 24xz^2 - 6xy^2 + 12xyz + 8y^2z - 16yz^2)

= > -6(3x(3xy - 6xz - 4yz + 8z^2) - 2y(3xy - 6xz - 4yz + 8z^2))

= > -6(3x - 2y)(3xy - 6xz - 4yz + 8z^2)

= > -6(3x - 2y)(3x(y - 2z) - 4z(y - 2z))

= > -6(3x - 2y)(3x - 4z)(y - 2z).