Factorize the following expressions: (2x - 3y)^3 + (4z - 2x)^3+ (… - Vidyadip

Question

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

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Answer

$(2x - 3y)^3 + (4z - 2x)^3+ (3y - 4z)^3$
Let $2x - 3y = a, 4z - 2x = b, 3y - 4z = c$
$\therefore$ $a + b + c = 2x - 3y + 4z - 2x + 3y - 4z = 0$
$\because$ $a + b + c = 0$
$\therefore$ $a^3 + b^3 + c^3 = 3abc$
$\therefore$ $(2x - 3y)^3 + (4z - 2x)^3+ (3y - 4z)^3$
$= 3(2x - 3y)(4z - 2x)(3y - 4z)$

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