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

Given:

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

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,

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

Therefore,

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

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