Factorize each of the following expressions:$(3x - 2y)^3 + (2y - 4z)^3 + (4z - 3x)^3$

Given:

$(3x - 2y)^3 + (2y - 4z)^3 + (4z - 3x)^3$

To do:

We have to multiply the given expressions.

Solution:

We know that,

$a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - ab - bc - ca)$

$a^3 + b^3 + c^3 = 3abc$ if $a + b + c = 0$

Here,

$3x - 2y + 2y - 4z + 4z - 3x = 0$

Therefore,

$(3x - 2y)^3 + (2y - 4z)^3 +   (4z - 3x)^3 = 3(3x - 2y) (2y - 4z) (4z - 3x)$

Hence, $(3x - 2y)^3 + (2y - 4z)^3 +   (4z - 3x)^3 = 3(3x - 2y) (2y - 4z) (4z - 3x)$.